{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**<div style=\"text-align: center\"><font color='#dc2624' face='微软雅黑' size = \"6\">线性回归与曲线分离</font></div>**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from IPython.core.interactiveshell import InteractiveShell\n",
    "InteractiveShell.ast_node_interactivity = \"all\" # 代码块显示所有执行结果"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**<div style=\"text-align: left\"><font color='black' face='微软雅黑' size = \"6\">引言</font><a name='top'></a></div>**\n",
    "\n",
    "* 通过线性回归，分别对每个国家人均预期寿命建模。\n",
    "* 然后通过分析残差，提出来筛选$R^2$较小或RMSE较大的模型，及对应的国家和数据。\n",
    "* $R^2$(拟合优度)低就就表示模型质量差，曲线波动剧烈。RMSE较大就表示误差较大。\n",
    "* 通过对模型斜率正负的判断，可以将上升趋势和下降趋势的曲线给分离出来，分别建模，提高模型质量，绘图也更加美观，避免曲线交叉。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "toc": true
   },
   "source": [
    "<h1>Table of Contents<span class=\"tocSkip\"></span></h1>\n",
    "<div class=\"toc\"><ul class=\"toc-item\"><li><span><a href=\"#需要的包\" data-toc-modified-id=\"需要的包-1\"><span class=\"toc-item-num\">1&nbsp;&nbsp;</span>需要的包</a></span></li><li><span><a href=\"#数据集\" data-toc-modified-id=\"数据集-2\"><span class=\"toc-item-num\">2&nbsp;&nbsp;</span>数据集</a></span></li><li><span><a href=\"#EDA\" data-toc-modified-id=\"EDA-3\"><span class=\"toc-item-num\">3&nbsp;&nbsp;</span>EDA</a></span></li><li><span><a href=\"#回归模型\" data-toc-modified-id=\"回归模型-4\"><span class=\"toc-item-num\">4&nbsp;&nbsp;</span>回归模型</a></span><ul class=\"toc-item\"><li><span><a href=\"#残差分析\" data-toc-modified-id=\"残差分析-4.1\"><span class=\"toc-item-num\">4.1&nbsp;&nbsp;</span>残差分析</a></span></li><li><span><a href=\"#$R^2$分析\" data-toc-modified-id=\"$R^2$分析-4.2\"><span class=\"toc-item-num\">4.2&nbsp;&nbsp;</span>$R^2$分析</a></span></li><li><span><a href=\"#RMSE分析\" data-toc-modified-id=\"RMSE分析-4.3\"><span class=\"toc-item-num\">4.3&nbsp;&nbsp;</span>RMSE分析</a></span></li></ul></li><li><span><a href=\"#斜率与趋势\" data-toc-modified-id=\"斜率与趋势-5\"><span class=\"toc-item-num\">5&nbsp;&nbsp;</span>斜率与趋势</a></span></li></ul></div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 需要的包"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "            <div id=\"Uyr046\"></div>\n",
       "            <script type=\"text/javascript\" data-lets-plot-script=\"library\">\n",
       "                if(!window.letsPlotCallQueue) {\n",
       "                    window.letsPlotCallQueue = [];\n",
       "                }; \n",
       "                window.letsPlotCall = function(f) {\n",
       "                    window.letsPlotCallQueue.push(f);\n",
       "                };\n",
       "                (function() {\n",
       "                    var script = document.createElement(\"script\");\n",
       "                    script.type = \"text/javascript\";\n",
       "                    script.src = \"https://cdn.jsdelivr.net/gh/JetBrains/lets-plot@v2.2.0/js-package/distr/lets-plot.min.js\";\n",
       "                    script.onload = function() {\n",
       "                        window.letsPlotCall = function(f) {f();};\n",
       "                        window.letsPlotCallQueue.forEach(function(f) {f();});\n",
       "                        window.letsPlotCallQueue = [];\n",
       "                        \n",
       "                    };\n",
       "                    script.onerror = function(event) {\n",
       "                        window.letsPlotCall = function(f) {};    // noop\n",
       "                        window.letsPlotCallQueue = [];\n",
       "                        var div = document.createElement(\"div\");\n",
       "                        div.style.color = 'darkred';\n",
       "                        div.textContent = 'Error loading Lets-Plot JS';\n",
       "                        document.getElementById(\"Uyr046\").appendChild(div);\n",
       "                    };\n",
       "                    var e = document.getElementById(\"Uyr046\");\n",
       "                    e.appendChild(script);\n",
       "                })()\n",
       "            </script>\n",
       "            "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 数据处理\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "# 绘图\n",
    "from lets_plot import LetsPlot, ggplot, aes, geom_line, geom_point, geom_boxplot, geom_smooth, geom_jitter\n",
    "from lets_plot import scale_color_brewer, facet_wrap, ggsize\n",
    "LetsPlot.setup_html() # 默认开启JS交互模式\n",
    "# LetsPlot.setup_html(no_js=True) # 关闭JS交互模式\n",
    "\n",
    "# 建模\n",
    "import statsmodels.formula.api as smf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 数据集\n",
    "gapminder数据集，包含世界上大部分国家的GDP历史数据，人口数量，和人口预期寿命。来自R\n",
    "```R\n",
    "library(gapminder)\n",
    "str(gapminder)\n",
    "write.csv(gapminder, file='./gapminder.csv', na='NA', row.names = F)\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1704, 6)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>country</th>\n",
       "      <th>continent</th>\n",
       "      <th>year</th>\n",
       "      <th>lifeExp</th>\n",
       "      <th>pop</th>\n",
       "      <th>gdpPercap</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Afghanistan</td>\n",
       "      <td>Asia</td>\n",
       "      <td>1952</td>\n",
       "      <td>28.801</td>\n",
       "      <td>8425333</td>\n",
       "      <td>779.445314</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Afghanistan</td>\n",
       "      <td>Asia</td>\n",
       "      <td>1957</td>\n",
       "      <td>30.332</td>\n",
       "      <td>9240934</td>\n",
       "      <td>820.853030</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Afghanistan</td>\n",
       "      <td>Asia</td>\n",
       "      <td>1962</td>\n",
       "      <td>31.997</td>\n",
       "      <td>10267083</td>\n",
       "      <td>853.100710</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Afghanistan</td>\n",
       "      <td>Asia</td>\n",
       "      <td>1967</td>\n",
       "      <td>34.020</td>\n",
       "      <td>11537966</td>\n",
       "      <td>836.197138</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Afghanistan</td>\n",
       "      <td>Asia</td>\n",
       "      <td>1972</td>\n",
       "      <td>36.088</td>\n",
       "      <td>13079460</td>\n",
       "      <td>739.981106</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       country continent  year  lifeExp       pop   gdpPercap\n",
       "0  Afghanistan      Asia  1952   28.801   8425333  779.445314\n",
       "1  Afghanistan      Asia  1957   30.332   9240934  820.853030\n",
       "2  Afghanistan      Asia  1962   31.997  10267083  853.100710\n",
       "3  Afghanistan      Asia  1967   34.020  11537966  836.197138\n",
       "4  Afghanistan      Asia  1972   36.088  13079460  739.981106"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "country       object\n",
       "continent     object\n",
       "year           int64\n",
       "lifeExp      float64\n",
       "pop            int64\n",
       "gdpPercap    float64\n",
       "dtype: object"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gapminder_df1 = pd.read_csv('./gapminder.csv')\n",
    "gapminder_df1.shape # 1.7k行\n",
    "gapminder_df1.head()\n",
    "gapminder_df1.dtypes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "country      False\n",
       "continent    False\n",
       "year         False\n",
       "lifeExp      False\n",
       "pop          False\n",
       "gdpPercap    False\n",
       "dtype: bool"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gapminder_df1.isna().any(axis=0) # 查看缺失值\n",
    "# gapminder_df1.isna().sum(axis=0) # 缺失值数量\n",
    "# gapminder_df1.isna().agg(lambda x: x.sum(axis=0)/x.shape[0] * 100) # 缺失值比例"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>year</th>\n",
       "      <th>lifeExp</th>\n",
       "      <th>pop</th>\n",
       "      <th>gdpPercap</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>1704.00000</td>\n",
       "      <td>1704.000000</td>\n",
       "      <td>1.704000e+03</td>\n",
       "      <td>1704.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>1979.50000</td>\n",
       "      <td>59.474439</td>\n",
       "      <td>2.960121e+07</td>\n",
       "      <td>7215.327081</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>17.26533</td>\n",
       "      <td>12.917107</td>\n",
       "      <td>1.061579e+08</td>\n",
       "      <td>9857.454543</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>1952.00000</td>\n",
       "      <td>23.599000</td>\n",
       "      <td>6.001100e+04</td>\n",
       "      <td>241.165876</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>1965.75000</td>\n",
       "      <td>48.198000</td>\n",
       "      <td>2.793664e+06</td>\n",
       "      <td>1202.060309</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>1979.50000</td>\n",
       "      <td>60.712500</td>\n",
       "      <td>7.023596e+06</td>\n",
       "      <td>3531.846988</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>1993.25000</td>\n",
       "      <td>70.845500</td>\n",
       "      <td>1.958522e+07</td>\n",
       "      <td>9325.462346</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>2007.00000</td>\n",
       "      <td>82.603000</td>\n",
       "      <td>1.318683e+09</td>\n",
       "      <td>113523.132900</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             year      lifeExp           pop      gdpPercap\n",
       "count  1704.00000  1704.000000  1.704000e+03    1704.000000\n",
       "mean   1979.50000    59.474439  2.960121e+07    7215.327081\n",
       "std      17.26533    12.917107  1.061579e+08    9857.454543\n",
       "min    1952.00000    23.599000  6.001100e+04     241.165876\n",
       "25%    1965.75000    48.198000  2.793664e+06    1202.060309\n",
       "50%    1979.50000    60.712500  7.023596e+06    3531.846988\n",
       "75%    1993.25000    70.845500  1.958522e+07    9325.462346\n",
       "max    2007.00000    82.603000  1.318683e+09  113523.132900"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 统计数字变量分布\n",
    "gapminder_df1.describe(include='number')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "country      142\n",
       "continent      5\n",
       "dtype: int64"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "continent\n",
       "Africa      52\n",
       "Americas    25\n",
       "Asia        33\n",
       "Europe      30\n",
       "Oceania      2\n",
       "Name: country, dtype: int64"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gapminder_df1[['country', 'continent']].agg('nunique')\n",
    "\n",
    "# 每个大洲有多少个国家\n",
    "(gapminder_df1[['continent', 'country']].drop_duplicates()\n",
    " .set_index('continent')\n",
    " .groupby(level='continent')['country']\n",
    " .count()\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# EDA\n",
    "这里我们需要分析人口预期寿命(`lifeExp`)与时间(`year`)和国家(`country`)之间的关系。首先进行EDA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "   <div id=\"7TwfHI\"></div>\n",
       "   <script type=\"text/javascript\" data-lets-plot-script=\"plot\">\n",
       "       (function() {\n",
       "           var plotSpec={\n",
       "\"data\":{\n",
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       "},\n",
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       "\"group\":\"country\"\n",
       "},\n",
       "\"data_meta\":{\n",
       "},\n",
       "\"ggsize\":{\n",
       "\"width\":800,\n",
       "\"height\":400\n",
       "},\n",
       "\"kind\":\"plot\",\n",
       "\"scales\":[],\n",
       "\"layers\":[{\n",
       "\"geom\":\"line\",\n",
       "\"mapping\":{\n",
       "},\n",
       "\"data_meta\":{\n",
       "},\n",
       "\"color\":\"#4169E1\",\n",
       "\"alpha\":0.3333333333333333,\n",
       "\"data\":{\n",
       "}\n",
       "}]\n",
       "};\n",
       "           var plotContainer = document.getElementById(\"7TwfHI\");\n",
       "           window.letsPlotCall(function() {{\n",
       "               LetsPlot.buildPlotFromProcessedSpecs(plotSpec, -1, -1, plotContainer);\n",
       "           }});\n",
       "       })();    \n",
       "   </script>"
      ],
      "text/plain": [
       "<lets_plot.plot.core.PlotSpec at 0x250b0bbe648>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ggplot(gapminder_df1, aes(x='year', y='lifeExp', group='country')) \\\n",
    "+ geom_line(color='#4169E1', alpha=1/3) \\\n",
    "+ ggsize(800, 400)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "   <div id=\"Tr5xCb\"></div>\n",
       "   <script type=\"text/javascript\" data-lets-plot-script=\"plot\">\n",
       "       (function() {\n",
       "           var plotSpec={\n",
       "\"data\":{\n",
       "\"country\":[\"Afghanistan\",\"Afghanistan\",\"Afghanistan\",\"Afghanistan\",\"Afghanistan\",\"Afghanistan\",\"Afghanistan\",\"Afghanistan\",\"Afghanistan\",\"Afghanistan\",\"Afghanistan\",\"Afghanistan\",\"Albania\",\"Albania\",\"Albania\",\"Albania\",\"Albania\",\"Albania\",\"Albania\",\"Albania\",\"Albania\",\"Albania\",\"Albania\",\"Albania\",\"Algeria\",\"Algeria\",\"Algeria\",\"Algeria\",\"Algeria\",\"Algeria\",\"Algeria\",\"Algeria\",\"Algeria\",\"Algeria\",\"Algeria\",\"Algeria\",\"Angola\",\"Angola\",\"Angola\",\"Angola\",\"Angola\",\"Angola\",\"Angola\",\"Angola\",\"Angola\",\"Angola\",\"Angola\",\"Angola\",\"Argentina\",\"Argentina\",\"Argentina\",\"Argentina\",\"Argentina\",\"Argentina\",\"Argentina\",\"Argentina\",\"Argentina\",\"Argentina\",\"Argentina\",\"Argentina\",\"Australia\",\"Australia\",\"Australia\",\"Australia\",\"Australia\",\"Australia\",\"Australia\",\"Australia\",\"Australia\",\"Australia\",\"Australia\",\"Australia\",\"Austria\",\"Austria\",\"Austria\",\"Austria\",\"Austria\",\"Austria\",\"Austria\",\"Austria\",\"Austria\",\"Austria\",\"Austria\",\"Austria\",\"Bahrain\",\"Bahrain\",\"Bahrain\",\"Bahrain\",\"Bahrain\",\"Bahrain\",\"Bahrain\",\"Bahrain\",\"Bahrain\",\"Bahrain\",\"Bahrain\",\"Bahrain\",\"Bangladesh\",\"Bangladesh\",\"Bangladesh\",\"Bangladesh\",\"Bangladesh\",\"Bangladesh\",\"Bangladesh\",\"Bangladesh\",\"Bangladesh\",\"Bangladesh\",\"Bangladesh\",\"Bangladesh\",\"Belgium\",\"Belgium\",\"Belgium\",\"Belgium\",\"Belgium\",\"Belgium\",\"Belgium\",\"Belgium\",\"Belgium\",\"Belgium\",\"Belgium\",\"Belgium\",\"Benin\",\"Benin\",\"Benin\",\"Benin\",\"Benin\",\"Benin\",\"Benin\",\"Benin\",\"Benin\",\"Benin\",\"Benin\",\"Benin\",\"Bolivia\",\"Bolivia\",\"Bolivia\",\"Bolivia\",\"Bolivia\",\"Bolivia\",\"Bolivia\",\"Bolivia\",\"Bolivia\",\"Bolivia\",\"Bolivia\",\"Bolivia\",\"Bosnia and Herzegovina\",\"Bosnia and Herzegovina\",\"Bosnia and Herzegovina\",\"Bosnia and Herzegovina\",\"Bosnia and Herzegovina\",\"Bosnia and Herzegovina\",\"Bosnia and Herzegovina\",\"Bosnia and Herzegovina\",\"Bosnia and Herzegovina\",\"Bosnia and Herzegovina\",\"Bosnia and Herzegovina\",\"Bosnia and Herzegovina\",\"Botswana\",\"Botswana\",\"Botswana\",\"Botswana\",\"Botswana\",\"Botswana\",\"Botswana\",\"Botswana\",\"Botswana\",\"Botswana\",\"Botswana\",\"Botswana\",\"Brazil\",\"Brazil\",\"Brazil\",\"Brazil\",\"Brazil\",\"Brazil\",\"Brazil\",\"Brazil\",\"Brazil\",\"Brazil\",\"Brazil\",\"Brazil\",\"Bulgaria\",\"Bulgaria\",\"Bulgaria\",\"Bulgaria\",\"Bulgaria\",\"Bulgaria\",\"Bulgaria\",\"Bulgaria\",\"Bulgaria\",\"Bulgaria\",\"Bulgaria\",\"Bulgaria\",\"Burkina Faso\",\"Burkina Faso\",\"Burkina Faso\",\"Burkina Faso\",\"Burkina Faso\",\"Burkina Faso\",\"Burkina Faso\",\"Burkina Faso\",\"Burkina Faso\",\"Burkina Faso\",\"Burkina Faso\",\"Burkina Faso\",\"Burundi\",\"Burundi\",\"Burundi\",\"Burundi\",\"Burundi\",\"Burundi\",\"Burundi\",\"Burundi\",\"Burundi\",\"Burundi\",\"Burundi\",\"Burundi\",\"Cambodia\",\"Cambodia\",\"Cambodia\",\"Cambodia\",\"Cambodia\",\"Cambodia\",\"Cambodia\",\"Cambodia\",\"Cambodia\",\"Cambodia\",\"Cambodia\",\"Cambodia\",\"Cameroon\",\"Cameroon\",\"Cameroon\",\"Cameroon\",\"Cameroon\",\"Cameroon\",\"Cameroon\",\"Cameroon\",\"Cameroon\",\"Cameroon\",\"Cameroon\",\"Cameroon\",\"Canada\",\"Canada\",\"Canada\",\"Canada\",\"Canada\",\"Canada\",\"Canada\",\"Canada\",\"Canada\",\"Canada\",\"Canada\",\"Canada\",\"Central African Republic\",\"Central African Republic\",\"Central African Republic\",\"Central African Republic\",\"Central African Republic\",\"Central African Republic\",\"Central African Republic\",\"Central African Republic\",\"Central African Republic\",\"Central African Republic\",\"Central African Republic\",\"Central African Republic\",\"Chad\",\"Chad\",\"Chad\",\"Chad\",\"Chad\",\"Chad\",\"Chad\",\"Chad\",\"Chad\",\"Chad\",\"Chad\",\"Chad\",\"Chile\",\"Chile\",\"Chile\",\"Chile\",\"Chile\",\"Chile\",\"Chile\",\"Chile\",\"Chile\",\"Chile\",\"Chile\",\"Chile\",\"China\",\"China\",\"China\",\"China\",\"China\",\"China\",\"China\",\"China\",\"China\",\"China\",\"China\",\"China\",\"Colombia\",\"Colombia\",\"Colombia\",\"Colombia\",\"Colombia\",\"Colombia\",\"Colombia\",\"Colombia\",\"Colombia\",\"Colombia\",\"Colombia\",\"Colombia\",\"Comoros\",\"Comoros\",\"Comoros\",\"Comoros\",\"Comoros\",\"Comoros\",\"Comoros\",\"Comoros\",\"Comoros\",\"Comoros\",\"Comoros\",\"Comoros\",\"Congo, Dem. Rep.\",\"Congo, Dem. Rep.\",\"Congo, Dem. Rep.\",\"Congo, Dem. Rep.\",\"Congo, Dem. Rep.\",\"Congo, Dem. Rep.\",\"Congo, Dem. Rep.\",\"Congo, Dem. Rep.\",\"Congo, Dem. Rep.\",\"Congo, Dem. Rep.\",\"Congo, Dem. Rep.\",\"Congo, Dem. Rep.\",\"Congo, Rep.\",\"Congo, Rep.\",\"Congo, Rep.\",\"Congo, Rep.\",\"Congo, Rep.\",\"Congo, Rep.\",\"Congo, Rep.\",\"Congo, Rep.\",\"Congo, Rep.\",\"Congo, Rep.\",\"Congo, Rep.\",\"Congo, Rep.\",\"Costa Rica\",\"Costa Rica\",\"Costa Rica\",\"Costa Rica\",\"Costa Rica\",\"Costa Rica\",\"Costa Rica\",\"Costa Rica\",\"Costa Rica\",\"Costa Rica\",\"Costa Rica\",\"Costa Rica\",\"Cote d'Ivoire\",\"Cote d'Ivoire\",\"Cote d'Ivoire\",\"Cote d'Ivoire\",\"Cote d'Ivoire\",\"Cote d'Ivoire\",\"Cote d'Ivoire\",\"Cote d'Ivoire\",\"Cote d'Ivoire\",\"Cote d'Ivoire\",\"Cote d'Ivoire\",\"Cote d'Ivoire\",\"Croatia\",\"Croatia\",\"Croatia\",\"Croatia\",\"Croatia\",\"Croatia\",\"Croatia\",\"Croatia\",\"Croatia\",\"Croatia\",\"Croatia\",\"Croatia\",\"Cuba\",\"Cuba\",\"Cuba\",\"Cuba\",\"Cuba\",\"Cuba\",\"Cuba\",\"Cuba\",\"Cuba\",\"Cuba\",\"Cuba\",\"Cuba\",\"Czech Republic\",\"Czech Republic\",\"Czech Republic\",\"Czech Republic\",\"Czech Republic\",\"Czech Republic\",\"Czech Republic\",\"Czech Republic\",\"Czech Republic\",\"Czech Republic\",\"Czech Republic\",\"Czech Republic\",\"Denmark\",\"Denmark\",\"Denmark\",\"Denmark\",\"Denmark\",\"Denmark\",\"Denmark\",\"Denmark\",\"Denmark\",\"Denmark\",\"Denmark\",\"Denmark\",\"Djibouti\",\"Djibouti\",\"Djibouti\",\"Djibouti\",\"Djibouti\",\"Djibouti\",\"Djibouti\",\"Djibouti\",\"Djibouti\",\"Djibouti\",\"Djibouti\",\"Djibouti\",\"Dominican Republic\",\"Dominican Republic\",\"Dominican Republic\",\"Dominican Republic\",\"Dominican Republic\",\"Dominican Republic\",\"Dominican Republic\",\"Dominican Republic\",\"Dominican Republic\",\"Dominican Republic\",\"Dominican Republic\",\"Dominican Republic\",\"Ecuador\",\"Ecuador\",\"Ecuador\",\"Ecuador\",\"Ecuador\",\"Ecuador\",\"Ecuador\",\"Ecuador\",\"Ecuador\",\"Ecuador\",\"Ecuador\",\"Ecuador\",\"Egypt\",\"Egypt\",\"Egypt\",\"Egypt\",\"Egypt\",\"Egypt\",\"Egypt\",\"Egypt\",\"Egypt\",\"Egypt\",\"Egypt\",\"Egypt\",\"El Salvador\",\"El Salvador\",\"El Salvador\",\"El Salvador\",\"El 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Kong, China\",\"Hong Kong, China\",\"Hong Kong, China\",\"Hong Kong, China\",\"Hong Kong, China\",\"Hong Kong, China\",\"Hong Kong, China\",\"Hong Kong, China\",\"Hong Kong, China\",\"Hong Kong, China\",\"Hong Kong, China\",\"Hong Kong, China\",\"Hungary\",\"Hungary\",\"Hungary\",\"Hungary\",\"Hungary\",\"Hungary\",\"Hungary\",\"Hungary\",\"Hungary\",\"Hungary\",\"Hungary\",\"Hungary\",\"Iceland\",\"Iceland\",\"Iceland\",\"Iceland\",\"Iceland\",\"Iceland\",\"Iceland\",\"Iceland\",\"Iceland\",\"Iceland\",\"Iceland\",\"Iceland\",\"India\",\"India\",\"India\",\"India\",\"India\",\"India\",\"India\",\"India\",\"India\",\"India\",\"India\",\"India\",\"Indonesia\",\"Indonesia\",\"Indonesia\",\"Indonesia\",\"Indonesia\",\"Indonesia\",\"Indonesia\",\"Indonesia\",\"Indonesia\",\"Indonesia\",\"Indonesia\",\"Indonesia\",\"Iran\",\"Iran\",\"Iran\",\"Iran\",\"Iran\",\"Iran\",\"Iran\",\"Iran\",\"Iran\",\"Iran\",\"Iran\",\"Iran\",\"Iraq\",\"Iraq\",\"Iraq\",\"Iraq\",\"Iraq\",\"Iraq\",\"Iraq\",\"Iraq\",\"Iraq\",\"Iraq\",\"Iraq\",\"Iraq\",\"Ireland\",\"Ireland\",\"Ireland\",\"Ireland\",\"Ireland\",\"Ireland\",\"Ireland\",\"Ireland\",\"Ireland\",\"Ireland\",\"Ireland\",\"Ireland\",\"Israel\",\"Israel\",\"Israel\",\"Israel\",\"Israel\",\"Israel\",\"Israel\",\"Israel\",\"Israel\",\"Israel\",\"Israel\",\"Israel\",\"Italy\",\"Italy\",\"Italy\",\"Italy\",\"Italy\",\"Italy\",\"Italy\",\"Italy\",\"Italy\",\"Italy\",\"Italy\",\"Italy\",\"Jamaica\",\"Jamaica\",\"Jamaica\",\"Jamaica\",\"Jamaica\",\"Jamaica\",\"Jamaica\",\"Jamaica\",\"Jamaica\",\"Jamaica\",\"Jamaica\",\"Jamaica\",\"Japan\",\"Japan\",\"Japan\",\"Japan\",\"Japan\",\"Japan\",\"Japan\",\"Japan\",\"Japan\",\"Japan\",\"Japan\",\"Japan\",\"Jordan\",\"Jordan\",\"Jordan\",\"Jordan\",\"Jordan\",\"Jordan\",\"Jordan\",\"Jordan\",\"Jordan\",\"Jordan\",\"Jordan\",\"Jordan\",\"Kenya\",\"Kenya\",\"Kenya\",\"Kenya\",\"Kenya\",\"Kenya\",\"Kenya\",\"Kenya\",\"Kenya\",\"Kenya\",\"Kenya\",\"Kenya\",\"Korea, Dem. Rep.\",\"Korea, Dem. Rep.\",\"Korea, Dem. Rep.\",\"Korea, Dem. Rep.\",\"Korea, Dem. Rep.\",\"Korea, Dem. Rep.\",\"Korea, Dem. Rep.\",\"Korea, Dem. Rep.\",\"Korea, Dem. Rep.\",\"Korea, Dem. Rep.\",\"Korea, Dem. Rep.\",\"Korea, Dem. Rep.\",\"Korea, Rep.\",\"Korea, Rep.\",\"Korea, Rep.\",\"Korea, Rep.\",\"Korea, Rep.\",\"Korea, Rep.\",\"Korea, Rep.\",\"Korea, Rep.\",\"Korea, Rep.\",\"Korea, Rep.\",\"Korea, Rep.\",\"Korea, Rep.\",\"Kuwait\",\"Kuwait\",\"Kuwait\",\"Kuwait\",\"Kuwait\",\"Kuwait\",\"Kuwait\",\"Kuwait\",\"Kuwait\",\"Kuwait\",\"Kuwait\",\"Kuwait\",\"Lebanon\",\"Lebanon\",\"Lebanon\",\"Lebanon\",\"Lebanon\",\"Lebanon\",\"Lebanon\",\"Lebanon\",\"Lebanon\",\"Lebanon\",\"Lebanon\",\"Lebanon\",\"Lesotho\",\"Lesotho\",\"Lesotho\",\"Lesotho\",\"Lesotho\",\"Lesotho\",\"Lesotho\",\"Lesotho\",\"Lesotho\",\"Lesotho\",\"Lesotho\",\"Lesotho\",\"Liberia\",\"Liberia\",\"Liberia\",\"Liberia\",\"Liberia\",\"Liberia\",\"Liberia\",\"Liberia\",\"Liberia\",\"Liberia\",\"Liberia\",\"Liberia\",\"Libya\",\"Libya\",\"Libya\",\"Libya\",\"Libya\",\"Libya\",\"Libya\",\"Libya\",\"Libya\",\"Libya\",\"Libya\",\"Libya\",\"Madagascar\",\"Madagascar\",\"Madagascar\",\"Madagascar\",\"Madagascar\",\"Madagascar\",\"Madagascar\",\"Madagascar\",\"Madagascar\",\"Madagascar\",\"Madagascar\",\"Madagascar\",\"Malawi\",\"Malawi\",\"Malawi\",\"Malawi\",\"Malawi\",\"Malawi\",\"Malawi\",\"Malawi\",\"Malawi\",\"Malawi\",\"Malawi\",\"Malawi\",\"Malaysia\",\"Malaysia\",\"Malaysia\",\"Malaysia\",\"Malaysia\",\"Malaysia\",\"Malaysia\",\"Malaysia\",\"Malaysia\",\"Malaysia\",\"Malaysia\",\"Malaysia\",\"Mali\",\"Mali\",\"Mali\",\"Mali\",\"Mali\",\"Mali\",\"Mali\",\"Mali\",\"Mali\",\"Mali\",\"Mali\",\"Mali\",\"Mauritania\",\"Mauritania\",\"Mauritania\",\"Mauritania\",\"Mauritania\",\"Mauritania\",\"Mauritania\",\"Mauritania\",\"Mauritania\",\"Mauritania\",\"Mauritania\",\"Mauritania\",\"Mauritius\",\"Mauritius\",\"Mauritius\",\"Mauritius\",\"Mauritius\",\"Mauritius\",\"Mauritius\",\"Mauritius\",\"Mauritius\",\"Mauritius\",\"Mauritius\",\"Mauritius\",\"Mexico\",\"Mexico\",\"Mexico\",\"Mexico\",\"Mexico\",\"Mexico\",\"Mexico\",\"Mexico\",\"Mexico\",\"Mexico\",\"Mexico\",\"Mexico\",\"Mongolia\",\"Mongolia\",\"Mongolia\",\"Mongolia\",\"Mongolia\",\"Mongolia\",\"Mongolia\",\"Mongolia\",\"Mongolia\",\"Mongolia\",\"Mongolia\",\"Mongolia\",\"Montenegro\",\"Montenegro\",\"Montenegro\",\"Montenegro\",\"Montenegro\",\"Montenegro\",\"Montenegro\",\"Montenegro\",\"Montenegro\",\"Montenegro\",\"Montenegro\",\"Montenegro\",\"Morocco\",\"Morocco\",\"Morocco\",\"Morocco\",\"Morocco\",\"Morocco\",\"Morocco\",\"Morocco\",\"Morocco\",\"Morocco\",\"Morocco\",\"Morocco\",\"Mozambique\",\"Mozambique\",\"Mozambique\",\"Mozambique\",\"Mozambique\",\"Mozambique\",\"Mozambique\",\"Mozambique\",\"Mozambique\",\"Mozambique\",\"Mozambique\",\"Mozambique\",\"Myanmar\",\"Myanmar\",\"Myanmar\",\"Myanmar\",\"Myanmar\",\"Myanmar\",\"Myanmar\",\"Myanmar\",\"Myanmar\",\"Myanmar\",\"Myanmar\",\"Myanmar\",\"Namibia\",\"Namibia\",\"Namibia\",\"Namibia\",\"Namibia\",\"Namibia\",\"Namibia\",\"Namibia\",\"Namibia\",\"Namibia\",\"Namibia\",\"Namibia\",\"Nepal\",\"Nepal\",\"Nepal\",\"Nepal\",\"Nepal\",\"Nepal\",\"Nepal\",\"Nepal\",\"Nepal\",\"Nepal\",\"Nepal\",\"Nepal\",\"Netherlands\",\"Netherlands\",\"Netherlands\",\"Netherlands\",\"Netherlands\",\"Netherlands\",\"Netherlands\",\"Netherlands\",\"Netherlands\",\"Netherlands\",\"Netherlands\",\"Netherlands\",\"New Zealand\",\"New Zealand\",\"New Zealand\",\"New Zealand\",\"New Zealand\",\"New Zealand\",\"New Zealand\",\"New Zealand\",\"New Zealand\",\"New Zealand\",\"New Zealand\",\"New Zealand\",\"Nicaragua\",\"Nicaragua\",\"Nicaragua\",\"Nicaragua\",\"Nicaragua\",\"Nicaragua\",\"Nicaragua\",\"Nicaragua\",\"Nicaragua\",\"Nicaragua\",\"Nicaragua\",\"Nicaragua\",\"Niger\",\"Niger\",\"Niger\",\"Niger\",\"Niger\",\"Niger\",\"Niger\",\"Niger\",\"Niger\",\"Niger\",\"Niger\",\"Niger\",\"Nigeria\",\"Nigeria\",\"Nigeria\",\"Nigeria\",\"Nigeria\",\"Nigeria\",\"Nigeria\",\"Nigeria\",\"Nigeria\",\"Nigeria\",\"Nigeria\",\"Nigeria\",\"Norway\",\"Norway\",\"Norway\",\"Norway\",\"Norway\",\"Norway\",\"Norway\",\"Norway\",\"Norway\",\"Norway\",\"Norway\",\"Norway\",\"Oman\",\"Oman\",\"Oman\",\"Oman\",\"Oman\",\"Oman\",\"Oman\",\"Oman\",\"Oman\",\"Oman\",\"Oman\",\"Oman\",\"Pakistan\",\"Pakistan\",\"Pakistan\",\"Pakistan\",\"Pakistan\",\"Pakistan\",\"Pakistan\",\"Pakistan\",\"Pakistan\",\"Pakistan\",\"Pakistan\",\"Pakistan\",\"Panama\",\"Panama\",\"Panama\",\"Panama\",\"Panama\",\"Panama\",\"Panama\",\"Panama\",\"Panama\",\"Panama\",\"Panama\",\"Panama\",\"Paraguay\",\"Paraguay\",\"Paraguay\",\"Paraguay\",\"Paraguay\",\"Paraguay\",\"Paraguay\",\"Paraguay\",\"Paraguay\",\"Paraguay\",\"Paraguay\",\"Paraguay\",\"Peru\",\"Peru\",\"Peru\",\"Peru\",\"Peru\",\"Peru\",\"Peru\",\"Peru\",\"Peru\",\"Peru\",\"Peru\",\"Peru\",\"Philippines\",\"Philippines\",\"Philippines\",\"Philippines\",\"Philippines\",\"Philippines\",\"Philippines\",\"Philippines\",\"Philippines\",\"Philippines\",\"Philippines\",\"Philippines\",\"Poland\",\"Poland\",\"Poland\",\"Poland\",\"Poland\",\"Poland\",\"Poland\",\"Poland\",\"Poland\",\"Poland\",\"Poland\",\"Poland\",\"Portugal\",\"Portugal\",\"Portugal\",\"Portugal\",\"Portugal\",\"Portugal\",\"Portugal\",\"Portugal\",\"Portugal\",\"Portugal\",\"Portugal\",\"Portugal\",\"Puerto Rico\",\"Puerto Rico\",\"Puerto Rico\",\"Puerto Rico\",\"Puerto Rico\",\"Puerto Rico\",\"Puerto Rico\",\"Puerto Rico\",\"Puerto Rico\",\"Puerto Rico\",\"Puerto Rico\",\"Puerto Rico\",\"Reunion\",\"Reunion\",\"Reunion\",\"Reunion\",\"Reunion\",\"Reunion\",\"Reunion\",\"Reunion\",\"Reunion\",\"Reunion\",\"Reunion\",\"Reunion\",\"Romania\",\"Romania\",\"Romania\",\"Romania\",\"Romania\",\"Romania\",\"Romania\",\"Romania\",\"Romania\",\"Romania\",\"Romania\",\"Romania\",\"Rwanda\",\"Rwanda\",\"Rwanda\",\"Rwanda\",\"Rwanda\",\"Rwanda\",\"Rwanda\",\"Rwanda\",\"Rwanda\",\"Rwanda\",\"Rwanda\",\"Rwanda\",\"Sao Tome and Principe\",\"Sao Tome and Principe\",\"Sao Tome and Principe\",\"Sao Tome and Principe\",\"Sao Tome and Principe\",\"Sao Tome and Principe\",\"Sao Tome and Principe\",\"Sao Tome and Principe\",\"Sao Tome and Principe\",\"Sao Tome and Principe\",\"Sao Tome and Principe\",\"Sao Tome and Principe\",\"Saudi Arabia\",\"Saudi Arabia\",\"Saudi Arabia\",\"Saudi Arabia\",\"Saudi Arabia\",\"Saudi Arabia\",\"Saudi Arabia\",\"Saudi Arabia\",\"Saudi Arabia\",\"Saudi Arabia\",\"Saudi Arabia\",\"Saudi Arabia\",\"Senegal\",\"Senegal\",\"Senegal\",\"Senegal\",\"Senegal\",\"Senegal\",\"Senegal\",\"Senegal\",\"Senegal\",\"Senegal\",\"Senegal\",\"Senegal\",\"Serbia\",\"Serbia\",\"Serbia\",\"Serbia\",\"Serbia\",\"Serbia\",\"Serbia\",\"Serbia\",\"Serbia\",\"Serbia\",\"Serbia\",\"Serbia\",\"Sierra Leone\",\"Sierra Leone\",\"Sierra Leone\",\"Sierra Leone\",\"Sierra Leone\",\"Sierra Leone\",\"Sierra Leone\",\"Sierra Leone\",\"Sierra Leone\",\"Sierra Leone\",\"Sierra Leone\",\"Sierra Leone\",\"Singapore\",\"Singapore\",\"Singapore\",\"Singapore\",\"Singapore\",\"Singapore\",\"Singapore\",\"Singapore\",\"Singapore\",\"Singapore\",\"Singapore\",\"Singapore\",\"Slovak Republic\",\"Slovak Republic\",\"Slovak Republic\",\"Slovak Republic\",\"Slovak Republic\",\"Slovak Republic\",\"Slovak Republic\",\"Slovak Republic\",\"Slovak Republic\",\"Slovak Republic\",\"Slovak 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       "},\n",
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       "\"group\":\"country\"\n",
       "},\n",
       "\"data_meta\":{\n",
       "},\n",
       "\"facet\":{\n",
       "\"name\":\"wrap\",\n",
       "\"facets\":\"continent\",\n",
       "\"ncol\":3,\n",
       "\"order\":1,\n",
       "\"dir\":\"h\"\n",
       "},\n",
       "\"ggsize\":{\n",
       "\"width\":900,\n",
       "\"height\":500\n",
       "},\n",
       "\"kind\":\"plot\",\n",
       "\"scales\":[],\n",
       "\"layers\":[{\n",
       "\"geom\":\"line\",\n",
       "\"mapping\":{\n",
       "},\n",
       "\"data_meta\":{\n",
       "},\n",
       "\"color\":\"#4169E1\",\n",
       "\"alpha\":0.3333333333333333,\n",
       "\"data\":{\n",
       "}\n",
       "}]\n",
       "};\n",
       "           var plotContainer = document.getElementById(\"Tr5xCb\");\n",
       "           window.letsPlotCall(function() {{\n",
       "               LetsPlot.buildPlotFromProcessedSpecs(plotSpec, -1, -1, plotContainer);\n",
       "           }});\n",
       "       })();    \n",
       "   </script>"
      ],
      "text/plain": [
       "<lets_plot.plot.core.PlotSpec at 0x250b0bdeb48>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ggplot(gapminder_df1, aes(x='year', y='lifeExp', group='country')) \\\n",
    "+ geom_line(color='#4169E1', alpha=1/3) \\\n",
    "+ facet_wrap('continent', ncol=3) \\\n",
    "+ ggsize(900, 500)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "看起来波动剧烈的曲线大部分都发生在亚洲和非洲。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 回归模型"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "&emsp;&emsp;这个数据集只有1704个观测值和3个变量，但是仍然非常复杂，很难抓住脉络。 比如大多数国家的人口预期寿命都随时间而延长，但是有几个国家不符合这种模式，通过对每个国家的数据进行建模，然后筛选出$R^2$小或RMSE较大的国家，就能找到波动剧烈的曲线。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def country_model(df, formula):\n",
    "    return smf.ols(formula=formula, data=df).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>continent</th>\n",
       "      <th>country</th>\n",
       "      <th>data</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Africa</td>\n",
       "      <td>Algeria</td>\n",
       "      <td>country continent  year  lifeExp       pop...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Africa</td>\n",
       "      <td>Angola</td>\n",
       "      <td>country continent  year  lifeExp       pop ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Africa</td>\n",
       "      <td>Benin</td>\n",
       "      <td>country continent  year  lifeExp      pop ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Africa</td>\n",
       "      <td>Botswana</td>\n",
       "      <td>country continent  year  lifeExp      po...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Africa</td>\n",
       "      <td>Burkina Faso</td>\n",
       "      <td>country continent  year  lifeExp    ...</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  continent       country                                               data\n",
       "0    Africa       Algeria      country continent  year  lifeExp       pop...\n",
       "1    Africa        Angola     country continent  year  lifeExp       pop ...\n",
       "2    Africa         Benin      country continent  year  lifeExp      pop ...\n",
       "3    Africa      Botswana        country continent  year  lifeExp      po...\n",
       "4    Africa  Burkina Faso            country continent  year  lifeExp    ..."
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nest1 = pd.DataFrame(list(gapminder_df1.groupby(by=['continent', 'country'])), columns=['country', 'data'])\n",
    "nest1['continent'] = nest1['country'].map(lambda x: x[0])\n",
    "nest1['country'] = nest1['country'].map(lambda x: x[1])\n",
    "nest1 = nest1.reindex(['continent', 'country', 'data'], axis=1)\n",
    "nest1.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "自变量(endogenous)为'year', 因变量(exogenous)为'lifeExp'。如果数据量很大，就需要使用joblib进行并行运算。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Wall time: 421 ms\n"
     ]
    },
    {
     "data": {
      "text/html": [
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       "  <thead>\n",
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       "      <th></th>\n",
       "      <th>continent</th>\n",
       "      <th>country</th>\n",
       "      <th>data</th>\n",
       "      <th>mod</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Africa</td>\n",
       "      <td>Algeria</td>\n",
       "      <td>country continent  year  lifeExp       pop...</td>\n",
       "      <td>&lt;statsmodels.regression.linear_model.Regressio...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Africa</td>\n",
       "      <td>Angola</td>\n",
       "      <td>country continent  year  lifeExp       pop ...</td>\n",
       "      <td>&lt;statsmodels.regression.linear_model.Regressio...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Africa</td>\n",
       "      <td>Benin</td>\n",
       "      <td>country continent  year  lifeExp      pop ...</td>\n",
       "      <td>&lt;statsmodels.regression.linear_model.Regressio...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Africa</td>\n",
       "      <td>Botswana</td>\n",
       "      <td>country continent  year  lifeExp      po...</td>\n",
       "      <td>&lt;statsmodels.regression.linear_model.Regressio...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Africa</td>\n",
       "      <td>Burkina Faso</td>\n",
       "      <td>country continent  year  lifeExp    ...</td>\n",
       "      <td>&lt;statsmodels.regression.linear_model.Regressio...</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  continent       country                                               data  \\\n",
       "0    Africa       Algeria      country continent  year  lifeExp       pop...   \n",
       "1    Africa        Angola     country continent  year  lifeExp       pop ...   \n",
       "2    Africa         Benin      country continent  year  lifeExp      pop ...   \n",
       "3    Africa      Botswana        country continent  year  lifeExp      po...   \n",
       "4    Africa  Burkina Faso            country continent  year  lifeExp    ...   \n",
       "\n",
       "                                                 mod  \n",
       "0  <statsmodels.regression.linear_model.Regressio...  \n",
       "1  <statsmodels.regression.linear_model.Regressio...  \n",
       "2  <statsmodels.regression.linear_model.Regressio...  \n",
       "3  <statsmodels.regression.linear_model.Regressio...  \n",
       "4  <statsmodels.regression.linear_model.Regressio...  "
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%%time\n",
    "nest1['mod'] = nest1['data'].map(lambda x: country_model(x, 'lifeExp ~ year')) # \n",
    "nest1.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>continent</th>\n",
       "      <th>country</th>\n",
       "      <th>data</th>\n",
       "      <th>pred</th>\n",
       "      <th>resid</th>\n",
       "      <th>rsquared</th>\n",
       "      <th>rsquared_adj</th>\n",
       "      <th>f_pvalue</th>\n",
       "      <th>Intercept</th>\n",
       "      <th>slope</th>\n",
       "      <th>BIC</th>\n",
       "      <th>AIC</th>\n",
       "      <th>RMSE</th>\n",
       "      <th>MSE</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Africa</td>\n",
       "      <td>Algeria</td>\n",
       "      <td>country continent  year  lifeExp       pop...</td>\n",
       "      <td>24    43.374974\n",
       "25    46.221373\n",
       "26    49.06777...</td>\n",
       "      <td>24   -0.297974\n",
       "25   -0.536373\n",
       "26   -0.764772\n",
       "2...</td>\n",
       "      <td>0.985117</td>\n",
       "      <td>0.983629</td>\n",
       "      <td>1.808143e-10</td>\n",
       "      <td>-1067.859040</td>\n",
       "      <td>0.569280</td>\n",
       "      <td>43.554240</td>\n",
       "      <td>42.584427</td>\n",
       "      <td>1.750346</td>\n",
       "      <td>106.917029</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Africa</td>\n",
       "      <td>Angola</td>\n",
       "      <td>country continent  year  lifeExp       pop ...</td>\n",
       "      <td>36    32.126654\n",
       "37    33.173353\n",
       "38    34.22005...</td>\n",
       "      <td>36   -2.111654\n",
       "37   -1.174353\n",
       "38   -0.220052\n",
       "3...</td>\n",
       "      <td>0.887815</td>\n",
       "      <td>0.876596</td>\n",
       "      <td>4.593498e-06</td>\n",
       "      <td>-376.504753</td>\n",
       "      <td>0.209340</td>\n",
       "      <td>45.031670</td>\n",
       "      <td>44.061857</td>\n",
       "      <td>1.979675</td>\n",
       "      <td>16.042237</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Africa</td>\n",
       "      <td>Benin</td>\n",
       "      <td>country continent  year  lifeExp      pop ...</td>\n",
       "      <td>120    39.588513\n",
       "121    41.259677\n",
       "122    42.93...</td>\n",
       "      <td>120   -1.365513\n",
       "121   -0.901677\n",
       "122   -0.31284...</td>\n",
       "      <td>0.966602</td>\n",
       "      <td>0.963262</td>\n",
       "      <td>1.037138e-08</td>\n",
       "      <td>-612.834044</td>\n",
       "      <td>0.334233</td>\n",
       "      <td>40.700602</td>\n",
       "      <td>39.730789</td>\n",
       "      <td>1.379899</td>\n",
       "      <td>37.560727</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Africa</td>\n",
       "      <td>Botswana</td>\n",
       "      <td>country continent  year  lifeExp      po...</td>\n",
       "      <td>156    52.929115\n",
       "157    53.232458\n",
       "158    53.53...</td>\n",
       "      <td>156   -5.307115\n",
       "157   -3.614458\n",
       "158   -2.01580...</td>\n",
       "      <td>0.034023</td>\n",
       "      <td>-0.062574</td>\n",
       "      <td>5.660414e-01</td>\n",
       "      <td>-65.495858</td>\n",
       "      <td>0.060669</td>\n",
       "      <td>80.283273</td>\n",
       "      <td>79.313460</td>\n",
       "      <td>37.358712</td>\n",
       "      <td>35.158683</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Africa</td>\n",
       "      <td>Burkina Faso</td>\n",
       "      <td>country continent  year  lifeExp    ...</td>\n",
       "      <td>192    34.684692\n",
       "193    36.504566\n",
       "194    38.32...</td>\n",
       "      <td>192   -2.709692\n",
       "193   -1.598566\n",
       "194   -0.51044...</td>\n",
       "      <td>0.918711</td>\n",
       "      <td>0.910582</td>\n",
       "      <td>9.047506e-07</td>\n",
       "      <td>-675.794166</td>\n",
       "      <td>0.363975</td>\n",
       "      <td>54.030559</td>\n",
       "      <td>53.060746</td>\n",
       "      <td>4.190584</td>\n",
       "      <td>46.864865</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  continent       country                                               data  \\\n",
       "0    Africa       Algeria      country continent  year  lifeExp       pop...   \n",
       "1    Africa        Angola     country continent  year  lifeExp       pop ...   \n",
       "2    Africa         Benin      country continent  year  lifeExp      pop ...   \n",
       "3    Africa      Botswana        country continent  year  lifeExp      po...   \n",
       "4    Africa  Burkina Faso            country continent  year  lifeExp    ...   \n",
       "\n",
       "                                                pred  \\\n",
       "0  24    43.374974\n",
       "25    46.221373\n",
       "26    49.06777...   \n",
       "1  36    32.126654\n",
       "37    33.173353\n",
       "38    34.22005...   \n",
       "2  120    39.588513\n",
       "121    41.259677\n",
       "122    42.93...   \n",
       "3  156    52.929115\n",
       "157    53.232458\n",
       "158    53.53...   \n",
       "4  192    34.684692\n",
       "193    36.504566\n",
       "194    38.32...   \n",
       "\n",
       "                                               resid  rsquared  rsquared_adj  \\\n",
       "0  24   -0.297974\n",
       "25   -0.536373\n",
       "26   -0.764772\n",
       "2...  0.985117      0.983629   \n",
       "1  36   -2.111654\n",
       "37   -1.174353\n",
       "38   -0.220052\n",
       "3...  0.887815      0.876596   \n",
       "2  120   -1.365513\n",
       "121   -0.901677\n",
       "122   -0.31284...  0.966602      0.963262   \n",
       "3  156   -5.307115\n",
       "157   -3.614458\n",
       "158   -2.01580...  0.034023     -0.062574   \n",
       "4  192   -2.709692\n",
       "193   -1.598566\n",
       "194   -0.51044...  0.918711      0.910582   \n",
       "\n",
       "       f_pvalue    Intercept     slope        BIC        AIC       RMSE  \\\n",
       "0  1.808143e-10 -1067.859040  0.569280  43.554240  42.584427   1.750346   \n",
       "1  4.593498e-06  -376.504753  0.209340  45.031670  44.061857   1.979675   \n",
       "2  1.037138e-08  -612.834044  0.334233  40.700602  39.730789   1.379899   \n",
       "3  5.660414e-01   -65.495858  0.060669  80.283273  79.313460  37.358712   \n",
       "4  9.047506e-07  -675.794166  0.363975  54.030559  53.060746   4.190584   \n",
       "\n",
       "          MSE  \n",
       "0  106.917029  \n",
       "1   16.042237  \n",
       "2   37.560727  \n",
       "3   35.158683  \n",
       "4   46.864865  "
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nest1['pred'] = nest1['mod'].map(lambda x: x.fittedvalues) # 预测值\n",
    "nest1['resid'] = nest1['mod'].map(lambda x: x.resid) # 残差\n",
    "nest1['rsquared'] = nest1['mod'].map(lambda x: x.rsquared) # R方\n",
    "nest1['rsquared_adj'] = nest1['mod'].map(lambda x: x.rsquared_adj) # 调整R方\n",
    "nest1['f_pvalue'] = nest1['mod'].map(lambda x: x.f_pvalue) # f统计量p值\n",
    "nest1['Intercept'] = nest1['mod'].map(lambda x: x.params['Intercept']) # 截距\n",
    "nest1['slope'] = nest1['mod'].map(lambda x: x.params['year']) # 斜率/系数\n",
    "nest1['BIC'] = nest1['mod'].map(lambda x: x.bic) # BIC信息量\n",
    "nest1['AIC'] = nest1['mod'].map(lambda x: x.aic) # AIC信息量\n",
    "nest1['RMSE'] = nest1['mod'].map(lambda x: x.mse_resid) # mean squared error of the residuals\n",
    "nest1['MSE'] = nest1['mod'].map(lambda x: x.mse_total)\n",
    "nest1.drop('mod', axis=1, inplace=True)\n",
    "nest1.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 残差分析"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>country</th>\n",
       "      <th>continent</th>\n",
       "      <th>year</th>\n",
       "      <th>lifeExp</th>\n",
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       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Algeria</td>\n",
       "      <td>Africa</td>\n",
       "      <td>1952</td>\n",
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       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Algeria</td>\n",
       "      <td>Africa</td>\n",
       "      <td>1957</td>\n",
       "      <td>45.685</td>\n",
       "      <td>10270856</td>\n",
       "      <td>3013.976023</td>\n",
       "      <td>-0.536373</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Algeria</td>\n",
       "      <td>Africa</td>\n",
       "      <td>1962</td>\n",
       "      <td>48.303</td>\n",
       "      <td>11000948</td>\n",
       "      <td>2550.816880</td>\n",
       "      <td>-0.764772</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Algeria</td>\n",
       "      <td>Africa</td>\n",
       "      <td>1967</td>\n",
       "      <td>51.407</td>\n",
       "      <td>12760499</td>\n",
       "      <td>3246.991771</td>\n",
       "      <td>-0.507170</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Algeria</td>\n",
       "      <td>Africa</td>\n",
       "      <td>1972</td>\n",
       "      <td>54.518</td>\n",
       "      <td>14760787</td>\n",
       "      <td>4182.663766</td>\n",
       "      <td>-0.242569</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   country continent  year  lifeExp       pop    gdpPercap     resid\n",
       "0  Algeria    Africa  1952   43.077   9279525  2449.008185 -0.297974\n",
       "1  Algeria    Africa  1957   45.685  10270856  3013.976023 -0.536373\n",
       "2  Algeria    Africa  1962   48.303  11000948  2550.816880 -0.764772\n",
       "3  Algeria    Africa  1967   51.407  12760499  3246.991771 -0.507170\n",
       "4  Algeria    Africa  1972   54.518  14760787  4182.663766 -0.242569"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# unnest列表列\n",
    "resids_df = (nest1.reindex(['data', 'resid'], axis=1)\n",
    "             .apply(lambda x: x['data'].assign(resid=x['resid']), axis=1)\n",
    "             .to_list()\n",
    "            )\n",
    "resids_df = pd.concat(resids_df, axis=0, ignore_index=True)\n",
    "resids_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "   <div id=\"RLJTH1\"></div>\n",
       "   <script type=\"text/javascript\" data-lets-plot-script=\"plot\">\n",
       "       (function() {\n",
       "           var plotSpec={\n",
       "\"data\":{\n",
       "\"country\":[\"Algeria\",\"Algeria\",\"Algeria\",\"Algeria\",\"Algeria\",\"Algeria\",\"Algeria\",\"Algeria\",\"Algeria\",\"Algeria\",\"Algeria\",\"Algeria\",\"Angola\",\"Angola\",\"Angola\",\"Angola\",\"Angola\",\"Angola\",\"Angola\",\"Angola\",\"Angola\",\"Angola\",\"Angola\",\"Angola\",\"Benin\",\"Benin\",\"Benin\",\"Benin\",\"Benin\",\"Benin\",\"Benin\",\"Benin\",\"Benin\",\"Benin\",\"Benin\",\"Benin\",\"Botswana\",\"Botswana\",\"Botswana\",\"Botswana\",\"Botswana\",\"Botswana\",\"Botswana\",\"Botswana\",\"Botswana\",\"Botswana\",\"Botswana\",\"Botswana\",\"Burkina Faso\",\"Burkina Faso\",\"Burkina Faso\",\"Burkina Faso\",\"Burkina Faso\",\"Burkina Faso\",\"Burkina Faso\",\"Burkina Faso\",\"Burkina Faso\",\"Burkina Faso\",\"Burkina Faso\",\"Burkina Faso\",\"Burundi\",\"Burundi\",\"Burundi\",\"Burundi\",\"Burundi\",\"Burundi\",\"Burundi\",\"Burundi\",\"Burundi\",\"Burundi\",\"Burundi\",\"Burundi\",\"Cameroon\",\"Cameroon\",\"Cameroon\",\"Cameroon\",\"Cameroon\",\"Cameroon\",\"Cameroon\",\"Cameroon\",\"Cameroon\",\"Cameroon\",\"Cameroon\",\"Cameroon\",\"Central African Republic\",\"Central African Republic\",\"Central African Republic\",\"Central African Republic\",\"Central African Republic\",\"Central African Republic\",\"Central African Republic\",\"Central African Republic\",\"Central African Republic\",\"Central African Republic\",\"Central African Republic\",\"Central African Republic\",\"Chad\",\"Chad\",\"Chad\",\"Chad\",\"Chad\",\"Chad\",\"Chad\",\"Chad\",\"Chad\",\"Chad\",\"Chad\",\"Chad\",\"Comoros\",\"Comoros\",\"Comoros\",\"Comoros\",\"Comoros\",\"Comoros\",\"Comoros\",\"Comoros\",\"Comoros\",\"Comoros\",\"Comoros\",\"Comoros\",\"Congo, Dem. Rep.\",\"Congo, Dem. Rep.\",\"Congo, Dem. Rep.\",\"Congo, Dem. Rep.\",\"Congo, Dem. Rep.\",\"Congo, Dem. Rep.\",\"Congo, Dem. Rep.\",\"Congo, Dem. Rep.\",\"Congo, Dem. Rep.\",\"Congo, Dem. Rep.\",\"Congo, Dem. Rep.\",\"Congo, Dem. Rep.\",\"Congo, Rep.\",\"Congo, Rep.\",\"Congo, Rep.\",\"Congo, Rep.\",\"Congo, Rep.\",\"Congo, Rep.\",\"Congo, Rep.\",\"Congo, Rep.\",\"Congo, Rep.\",\"Congo, Rep.\",\"Congo, Rep.\",\"Congo, Rep.\",\"Cote d'Ivoire\",\"Cote d'Ivoire\",\"Cote d'Ivoire\",\"Cote d'Ivoire\",\"Cote d'Ivoire\",\"Cote d'Ivoire\",\"Cote d'Ivoire\",\"Cote d'Ivoire\",\"Cote d'Ivoire\",\"Cote d'Ivoire\",\"Cote d'Ivoire\",\"Cote d'Ivoire\",\"Djibouti\",\"Djibouti\",\"Djibouti\",\"Djibouti\",\"Djibouti\",\"Djibouti\",\"Djibouti\",\"Djibouti\",\"Djibouti\",\"Djibouti\",\"Djibouti\",\"Djibouti\",\"Egypt\",\"Egypt\",\"Egypt\",\"Egypt\",\"Egypt\",\"Egypt\",\"Egypt\",\"Egypt\",\"Egypt\",\"Egypt\",\"Egypt\",\"Egypt\",\"Equatorial Guinea\",\"Equatorial Guinea\",\"Equatorial Guinea\",\"Equatorial Guinea\",\"Equatorial Guinea\",\"Equatorial Guinea\",\"Equatorial Guinea\",\"Equatorial Guinea\",\"Equatorial Guinea\",\"Equatorial Guinea\",\"Equatorial Guinea\",\"Equatorial Guinea\",\"Eritrea\",\"Eritrea\",\"Eritrea\",\"Eritrea\",\"Eritrea\",\"Eritrea\",\"Eritrea\",\"Eritrea\",\"Eritrea\",\"Eritrea\",\"Eritrea\",\"Eritrea\",\"Ethiopia\",\"Ethiopia\",\"Ethiopia\",\"Ethiopia\",\"Ethiopia\",\"Ethiopia\",\"Ethiopia\",\"Ethiopia\",\"Ethiopia\",\"Ethiopia\",\"Ethiopia\",\"Ethiopia\",\"Gabon\",\"Gabon\",\"Gabon\",\"Gabon\",\"Gabon\",\"Gabon\",\"Gabon\",\"Gabon\",\"Gabon\",\"Gabon\",\"Gabon\",\"Gabon\",\"Gambia\",\"Gambia\",\"Gambia\",\"Gambia\",\"Gambia\",\"Gambia\",\"Gambia\",\"Gambia\",\"Gambia\",\"Gambia\",\"Gambia\",\"Gambia\",\"Ghana\",\"Ghana\",\"Ghana\",\"Ghana\",\"Ghana\",\"Ghana\",\"Ghana\",\"Ghana\",\"Ghana\",\"Ghana\",\"Ghana\",\"Ghana\",\"Guinea\",\"Guinea\",\"Guinea\",\"Guinea\",\"Guinea\",\"Guinea\",\"Guinea\",\"Guinea\",\"Guinea\",\"Guinea\",\"Guinea\",\"Guinea\",\"Guinea-Bissau\",\"Guinea-Bissau\",\"Guinea-Bissau\",\"Guinea-Bissau\",\"Guinea-Bissau\",\"Guinea-Bissau\",\"Guinea-Bissau\",\"Guinea-Bissau\",\"Guinea-Bissau\",\"Guinea-Bissau\",\"Guinea-Bissau\",\"Guinea-Bissau\",\"Kenya\",\"Kenya\",\"Kenya\",\"Kenya\",\"Kenya\",\"Kenya\",\"Kenya\",\"Kenya\",\"Kenya\",\"Kenya\",\"Kenya\",\"Kenya\",\"Lesotho\",\"Lesotho\",\"Lesotho\",\"Lesotho\",\"Lesotho\",\"Lesotho\",\"Lesotho\",\"Lesotho\",\"Lesotho\",\"Lesotho\",\"Lesotho\",\"Lesotho\",\"Liberia\",\"Liberia\",\"Liberia\",\"Liberia\",\"Liberia\",\"Liberia\",\"Liberia\",\"Liberia\",\"Liberia\",\"Liberia\",\"Liberia\",\"Liberia\",\"Libya\",\"Libya\",\"Libya\",\"Libya\",\"Libya\",\"Libya\",\"Libya\",\"Libya\",\"Libya\",\"Libya\",\"Libya\",\"Libya\",\"Madagascar\",\"Madagascar\",\"Madagascar\",\"Madagascar\",\"Madagascar\",\"Madagascar\",\"Madagascar\",\"Madagascar\",\"Madagascar\",\"Madagascar\",\"Madagascar\",\"Madagascar\",\"Malawi\",\"Malawi\",\"Malawi\",\"Malawi\",\"Malawi\",\"Malawi\",\"Malawi\",\"Malawi\",\"Malawi\",\"Malawi\",\"Malawi\",\"Malawi\",\"Mali\",\"Mali\",\"Mali\",\"Mali\",\"Mali\",\"Mali\",\"Mali\",\"Mali\",\"Mali\",\"Mali\",\"Mali\",\"Mali\",\"Mauritania\",\"Mauritania\",\"Mauritania\",\"Mauritania\",\"Mauritania\",\"Mauritania\",\"Mauritania\",\"Mauritania\",\"Mauritania\",\"Mauritania\",\"Mauritania\",\"Mauritania\",\"Mauritius\",\"Mauritius\",\"Mauritius\",\"Mauritius\",\"Mauritius\",\"Mauritius\",\"Mauritius\",\"Mauritius\",\"Mauritius\",\"Mauritius\",\"Mauritius\",\"Mauritius\",\"Morocco\",\"Morocco\",\"Morocco\",\"Morocco\",\"Morocco\",\"Morocco\",\"Morocco\",\"Morocco\",\"Morocco\",\"Morocco\",\"Morocco\",\"Morocco\",\"Mozambique\",\"Mozambique\",\"Mozambique\",\"Mozambique\",\"Mozambique\",\"Mozambique\",\"Mozambique\",\"Mozambique\",\"Mozambique\",\"Mozambique\",\"Mozambique\",\"Mozambique\",\"Namibia\",\"Namibia\",\"Namibia\",\"Namibia\",\"Namibia\",\"Namibia\",\"Namibia\",\"Namibia\",\"Namibia\",\"Namibia\",\"Namibia\",\"Namibia\",\"Niger\",\"Niger\",\"Niger\",\"Niger\",\"Niger\",\"Niger\",\"Niger\",\"Niger\",\"Niger\",\"Niger\",\"Niger\",\"Niger\",\"Nigeria\",\"Nigeria\",\"Nigeria\",\"Nigeria\",\"Nigeria\",\"Nigeria\",\"Nigeria\",\"Nigeria\",\"Nigeria\",\"Nigeria\",\"Nigeria\",\"Nigeria\",\"Reunion\",\"Reunion\",\"Reunion\",\"Reunion\",\"Reunion\",\"Reunion\",\"Reunion\",\"Reunion\",\"Reunion\",\"Reunion\",\"Reunion\",\"Reunion\",\"Rwanda\",\"Rwanda\",\"Rwanda\",\"Rwanda\",\"Rwanda\",\"Rwanda\",\"Rwanda\",\"Rwanda\",\"Rwanda\",\"Rwanda\",\"Rwanda\",\"Rwanda\",\"Sao Tome and Principe\",\"Sao Tome and Principe\",\"Sao Tome and Principe\",\"Sao Tome and Principe\",\"Sao Tome and Principe\",\"Sao Tome and Principe\",\"Sao Tome and Principe\",\"Sao Tome and Principe\",\"Sao Tome and Principe\",\"Sao Tome and Principe\",\"Sao Tome and Principe\",\"Sao Tome and Principe\",\"Senegal\",\"Senegal\",\"Senegal\",\"Senegal\",\"Senegal\",\"Senegal\",\"Senegal\",\"Senegal\",\"Senegal\",\"Senegal\",\"Senegal\",\"Senegal\",\"Sierra Leone\",\"Sierra Leone\",\"Sierra Leone\",\"Sierra Leone\",\"Sierra Leone\",\"Sierra Leone\",\"Sierra Leone\",\"Sierra Leone\",\"Sierra Leone\",\"Sierra Leone\",\"Sierra Leone\",\"Sierra Leone\",\"Somalia\",\"Somalia\",\"Somalia\",\"Somalia\",\"Somalia\",\"Somalia\",\"Somalia\",\"Somalia\",\"Somalia\",\"Somalia\",\"Somalia\",\"Somalia\",\"South Africa\",\"South Africa\",\"South Africa\",\"South Africa\",\"South Africa\",\"South Africa\",\"South Africa\",\"South Africa\",\"South Africa\",\"South Africa\",\"South Africa\",\"South Africa\",\"Sudan\",\"Sudan\",\"Sudan\",\"Sudan\",\"Sudan\",\"Sudan\",\"Sudan\",\"Sudan\",\"Sudan\",\"Sudan\",\"Sudan\",\"Sudan\",\"Swaziland\",\"Swaziland\",\"Swaziland\",\"Swaziland\",\"Swaziland\",\"Swaziland\",\"Swaziland\",\"Swaziland\",\"Swaziland\",\"Swaziland\",\"Swaziland\",\"Swaziland\",\"Tanzania\",\"Tanzania\",\"Tanzania\",\"Tanzania\",\"Tanzania\",\"Tanzania\",\"Tanzania\",\"Tanzania\",\"Tanzania\",\"Tanzania\",\"Tanzania\",\"Tanzania\",\"Togo\",\"Togo\",\"Togo\",\"Togo\",\"Togo\",\"Togo\",\"Togo\",\"Togo\",\"Togo\",\"Togo\",\"Togo\",\"Togo\",\"Tunisia\",\"Tunisia\",\"Tunisia\",\"Tunisia\",\"Tunisia\",\"Tunisia\",\"Tunisia\",\"Tunisia\",\"Tunisia\",\"Tunisia\",\"Tunisia\",\"Tunisia\",\"Uganda\",\"Uganda\",\"Uganda\",\"Uganda\",\"Uganda\",\"Uganda\",\"Uganda\",\"Uganda\",\"Uganda\",\"Uganda\",\"Uganda\",\"Uganda\",\"Zambia\",\"Zambia\",\"Zambia\",\"Zambia\",\"Zambia\",\"Zambia\",\"Zambia\",\"Zambia\",\"Zambia\",\"Zambia\",\"Zambia\",\"Zambia\",\"Zimbabwe\",\"Zimbabwe\",\"Zimbabwe\",\"Zimbabwe\",\"Zimbabwe\",\"Zimbabwe\",\"Zimbabwe\",\"Zimbabwe\",\"Zimbabwe\",\"Zimbabwe\",\"Zimbabwe\",\"Zimbabwe\",\"Argentina\",\"Argentina\",\"Argentina\",\"Argentina\",\"Argentina\",\"Argentina\",\"Argentina\",\"Argentina\",\"Argentina\",\"Argentina\",\"Argentina\",\"Argentina\",\"Bolivia\",\"Bolivia\",\"Bolivia\",\"Bolivia\",\"Bolivia\",\"Bolivia\",\"Bolivia\",\"Bolivia\",\"Bolivia\",\"Bolivia\",\"Bolivia\",\"Bolivia\",\"Brazil\",\"Brazil\",\"Brazil\",\"Brazil\",\"Brazil\",\"Brazil\",\"Brazil\",\"Brazil\",\"Brazil\",\"Brazil\",\"Brazil\",\"Brazil\",\"Canada\",\"Canada\",\"Canada\",\"Canada\",\"Canada\",\"Canada\",\"Canada\",\"Canada\",\"Canada\",\"Canada\",\"Canada\",\"Canada\",\"Chile\",\"Chile\",\"Chile\",\"Chile\",\"Chile\",\"Chile\",\"Chile\",\"Chile\",\"Chile\",\"Chile\",\"Chile\",\"Chile\",\"Colombia\",\"Colombia\",\"Colombia\",\"Colombia\",\"Colombia\",\"Colombia\",\"Colombia\",\"Colombia\",\"Colombia\",\"Colombia\",\"Colombia\",\"Colombia\",\"Costa Rica\",\"Costa Rica\",\"Costa Rica\",\"Costa Rica\",\"Costa Rica\",\"Costa Rica\",\"Costa Rica\",\"Costa Rica\",\"Costa Rica\",\"Costa Rica\",\"Costa Rica\",\"Costa Rica\",\"Cuba\",\"Cuba\",\"Cuba\",\"Cuba\",\"Cuba\",\"Cuba\",\"Cuba\",\"Cuba\",\"Cuba\",\"Cuba\",\"Cuba\",\"Cuba\",\"Dominican Republic\",\"Dominican Republic\",\"Dominican Republic\",\"Dominican Republic\",\"Dominican Republic\",\"Dominican Republic\",\"Dominican Republic\",\"Dominican Republic\",\"Dominican Republic\",\"Dominican Republic\",\"Dominican Republic\",\"Dominican Republic\",\"Ecuador\",\"Ecuador\",\"Ecuador\",\"Ecuador\",\"Ecuador\",\"Ecuador\",\"Ecuador\",\"Ecuador\",\"Ecuador\",\"Ecuador\",\"Ecuador\",\"Ecuador\",\"El Salvador\",\"El Salvador\",\"El Salvador\",\"El Salvador\",\"El Salvador\",\"El Salvador\",\"El Salvador\",\"El Salvador\",\"El Salvador\",\"El Salvador\",\"El Salvador\",\"El Salvador\",\"Guatemala\",\"Guatemala\",\"Guatemala\",\"Guatemala\",\"Guatemala\",\"Guatemala\",\"Guatemala\",\"Guatemala\",\"Guatemala\",\"Guatemala\",\"Guatemala\",\"Guatemala\",\"Haiti\",\"Haiti\",\"Haiti\",\"Haiti\",\"Haiti\",\"Haiti\",\"Haiti\",\"Haiti\",\"Haiti\",\"Haiti\",\"Haiti\",\"Haiti\",\"Honduras\",\"Honduras\",\"Honduras\",\"Honduras\",\"Honduras\",\"Honduras\",\"Honduras\",\"Honduras\",\"Honduras\",\"Honduras\",\"Honduras\",\"Honduras\",\"Jamaica\",\"Jamaica\",\"Jamaica\",\"Jamaica\",\"Jamaica\",\"Jamaica\",\"Jamaica\",\"Jamaica\",\"Jamaica\",\"Jamaica\",\"Jamaica\",\"Jamaica\",\"Mexico\",\"Mexico\",\"Mexico\",\"Mexico\",\"Mexico\",\"Mexico\",\"Mexico\",\"Mexico\",\"Mexico\",\"Mexico\",\"Mexico\",\"Mexico\",\"Nicaragua\",\"Nicaragua\",\"Nicaragua\",\"Nicaragua\",\"Nicaragua\",\"Nicaragua\",\"Nicaragua\",\"Nicaragua\",\"Nicaragua\",\"Nicaragua\",\"Nicaragua\",\"Nicaragua\",\"Panama\",\"Panama\",\"Panama\",\"Panama\",\"Panama\",\"Panama\",\"Panama\",\"Panama\",\"Panama\",\"Panama\",\"Panama\",\"Panama\",\"Paraguay\",\"Paraguay\",\"Paraguay\",\"Paraguay\",\"Paraguay\",\"Paraguay\",\"Paraguay\",\"Paraguay\",\"Paraguay\",\"Paraguay\",\"Paraguay\",\"Paraguay\",\"Peru\",\"Peru\",\"Peru\",\"Peru\",\"Peru\",\"Peru\",\"Peru\",\"Peru\",\"Peru\",\"Peru\",\"Peru\",\"Peru\",\"Puerto Rico\",\"Puerto Rico\",\"Puerto Rico\",\"Puerto Rico\",\"Puerto Rico\",\"Puerto Rico\",\"Puerto Rico\",\"Puerto Rico\",\"Puerto Rico\",\"Puerto Rico\",\"Puerto Rico\",\"Puerto Rico\",\"Trinidad and Tobago\",\"Trinidad and Tobago\",\"Trinidad and Tobago\",\"Trinidad and Tobago\",\"Trinidad and Tobago\",\"Trinidad and Tobago\",\"Trinidad and Tobago\",\"Trinidad and Tobago\",\"Trinidad and Tobago\",\"Trinidad and Tobago\",\"Trinidad and Tobago\",\"Trinidad and Tobago\",\"United States\",\"United States\",\"United States\",\"United States\",\"United States\",\"United States\",\"United States\",\"United States\",\"United States\",\"United States\",\"United States\",\"United States\",\"Uruguay\",\"Uruguay\",\"Uruguay\",\"Uruguay\",\"Uruguay\",\"Uruguay\",\"Uruguay\",\"Uruguay\",\"Uruguay\",\"Uruguay\",\"Uruguay\",\"Uruguay\",\"Venezuela\",\"Venezuela\",\"Venezuela\",\"Venezuela\",\"Venezuela\",\"Venezuela\",\"Venezuela\",\"Venezuela\",\"Venezuela\",\"Venezuela\",\"Venezuela\",\"Venezuela\",\"Afghanistan\",\"Afghanistan\",\"Afghanistan\",\"Afghanistan\",\"Afghanistan\",\"Afghanistan\",\"Afghanistan\",\"Afghanistan\",\"Afghanistan\",\"Afghanistan\",\"Afghanistan\",\"Afghanistan\",\"Bahrain\",\"Bahrain\",\"Bahrain\",\"Bahrain\",\"Bahrain\",\"Bahrain\",\"Bahrain\",\"Bahrain\",\"Bahrain\",\"Bahrain\",\"Bahrain\",\"Bahrain\",\"Bangladesh\",\"Bangladesh\",\"Bangladesh\",\"Bangladesh\",\"Bangladesh\",\"Bangladesh\",\"Bangladesh\",\"Bangladesh\",\"Bangladesh\",\"Bangladesh\",\"Bangladesh\",\"Bangladesh\",\"Cambodia\",\"Cambodia\",\"Cambodia\",\"Cambodia\",\"Cambodia\",\"Cambodia\",\"Cambodia\",\"Cambodia\",\"Cambodia\",\"Cambodia\",\"Cambodia\",\"Cambodia\",\"China\",\"China\",\"China\",\"China\",\"China\",\"China\",\"China\",\"China\",\"China\",\"China\",\"China\",\"China\",\"Hong Kong, China\",\"Hong Kong, China\",\"Hong Kong, China\",\"Hong Kong, China\",\"Hong Kong, China\",\"Hong Kong, China\",\"Hong Kong, China\",\"Hong Kong, China\",\"Hong Kong, China\",\"Hong Kong, China\",\"Hong Kong, China\",\"Hong Kong, China\",\"India\",\"India\",\"India\",\"India\",\"India\",\"India\",\"India\",\"India\",\"India\",\"India\",\"India\",\"India\",\"Indonesia\",\"Indonesia\",\"Indonesia\",\"Indonesia\",\"Indonesia\",\"Indonesia\",\"Indonesia\",\"Indonesia\",\"Indonesia\",\"Indonesia\",\"Indonesia\",\"Indonesia\",\"Iran\",\"Iran\",\"Iran\",\"Iran\",\"Iran\",\"Iran\",\"Iran\",\"Iran\",\"Iran\",\"Iran\",\"Iran\",\"Iran\",\"Iraq\",\"Iraq\",\"Iraq\",\"Iraq\",\"Iraq\",\"Iraq\",\"Iraq\",\"Iraq\",\"Iraq\",\"Iraq\",\"Iraq\",\"Iraq\",\"Israel\",\"Israel\",\"Israel\",\"Israel\",\"Israel\",\"Israel\",\"Israel\",\"Israel\",\"Israel\",\"Israel\",\"Israel\",\"Israel\",\"Japan\",\"Japan\",\"Japan\",\"Japan\",\"Japan\",\"Japan\",\"Japan\",\"Japan\",\"Japan\",\"Japan\",\"Japan\",\"Japan\",\"Jordan\",\"Jordan\",\"Jordan\",\"Jordan\",\"Jordan\",\"Jordan\",\"Jordan\",\"Jordan\",\"Jordan\",\"Jordan\",\"Jordan\",\"Jordan\",\"Korea, Dem. Rep.\",\"Korea, Dem. Rep.\",\"Korea, Dem. Rep.\",\"Korea, Dem. Rep.\",\"Korea, Dem. Rep.\",\"Korea, Dem. Rep.\",\"Korea, Dem. Rep.\",\"Korea, Dem. Rep.\",\"Korea, Dem. Rep.\",\"Korea, Dem. Rep.\",\"Korea, Dem. Rep.\",\"Korea, Dem. Rep.\",\"Korea, Rep.\",\"Korea, Rep.\",\"Korea, Rep.\",\"Korea, Rep.\",\"Korea, Rep.\",\"Korea, Rep.\",\"Korea, Rep.\",\"Korea, Rep.\",\"Korea, Rep.\",\"Korea, Rep.\",\"Korea, Rep.\",\"Korea, Rep.\",\"Kuwait\",\"Kuwait\",\"Kuwait\",\"Kuwait\",\"Kuwait\",\"Kuwait\",\"Kuwait\",\"Kuwait\",\"Kuwait\",\"Kuwait\",\"Kuwait\",\"Kuwait\",\"Lebanon\",\"Lebanon\",\"Lebanon\",\"Lebanon\",\"Lebanon\",\"Lebanon\",\"Lebanon\",\"Lebanon\",\"Lebanon\",\"Lebanon\",\"Lebanon\",\"Lebanon\",\"Malaysia\",\"Malaysia\",\"Malaysia\",\"Malaysia\",\"Malaysia\",\"Malaysia\",\"Malaysia\",\"Malaysia\",\"Malaysia\",\"Malaysia\",\"Malaysia\",\"Malaysia\",\"Mongolia\",\"Mongolia\",\"Mongolia\",\"Mongolia\",\"Mongolia\",\"Mongolia\",\"Mongolia\",\"Mongolia\",\"Mongolia\",\"Mongolia\",\"Mongolia\",\"Mongolia\",\"Myanmar\",\"Myanmar\",\"Myanmar\",\"Myanmar\",\"Myanmar\",\"Myanmar\",\"Myanmar\",\"Myanmar\",\"Myanmar\",\"Myanmar\",\"Myanmar\",\"Myanmar\",\"Nepal\",\"Nepal\",\"Nepal\",\"Nepal\",\"Nepal\",\"Nepal\",\"Nepal\",\"Nepal\",\"Nepal\",\"Nepal\",\"Nepal\",\"Nepal\",\"Oman\",\"Oman\",\"Oman\",\"Oman\",\"Oman\",\"Oman\",\"Oman\",\"Oman\",\"Oman\",\"Oman\",\"Oman\",\"Oman\",\"Pakistan\",\"Pakistan\",\"Pakistan\",\"Pakistan\",\"Pakistan\",\"Pakistan\",\"Pakistan\",\"Pakistan\",\"Pakistan\",\"Pakistan\",\"Pakistan\",\"Pakistan\",\"Philippines\",\"Philippines\",\"Philippines\",\"Philippines\",\"Philippines\",\"Philippines\",\"Philippines\",\"Philippines\",\"Philippines\",\"Philippines\",\"Philippines\",\"Philippines\",\"Saudi Arabia\",\"Saudi Arabia\",\"Saudi Arabia\",\"Saudi Arabia\",\"Saudi Arabia\",\"Saudi Arabia\",\"Saudi Arabia\",\"Saudi Arabia\",\"Saudi Arabia\",\"Saudi Arabia\",\"Saudi Arabia\",\"Saudi Arabia\",\"Singapore\",\"Singapore\",\"Singapore\",\"Singapore\",\"Singapore\",\"Singapore\",\"Singapore\",\"Singapore\",\"Singapore\",\"Singapore\",\"Singapore\",\"Singapore\",\"Sri Lanka\",\"Sri Lanka\",\"Sri Lanka\",\"Sri Lanka\",\"Sri Lanka\",\"Sri Lanka\",\"Sri Lanka\",\"Sri Lanka\",\"Sri Lanka\",\"Sri Lanka\",\"Sri Lanka\",\"Sri 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       "\"year\":[1952.0,1952.6962025316457,1953.392405063291,1954.0886075949368,1954.7848101265822,1955.4810126582279,1956.1772151898733,1956.873417721519,1957.5696202531647,1958.26582278481,1958.9620253164558,1959.6582278481012,1960.3544303797469,1961.0506329113923,1961.746835443038,1962.4430379746836,1963.139240506329,1963.8354430379748,1964.5316455696202,1965.2278481012659,1965.9240506329113,1966.620253164557,1967.3164556962026,1968.012658227848,1968.7088607594937,1969.4050632911392,1970.1012658227849,1970.7974683544303,1971.493670886076,1972.1898734177216,1972.886075949367,1973.5822784810127,1974.2784810126582,1974.9746835443038,1975.6708860759493,1976.367088607595,1977.0632911392406,1977.759493670886,1978.4556962025317,1979.1518987341772,1979.8481012658228,1980.5443037974683,1981.240506329114,1981.9367088607596,1982.632911392405,1983.3291139240507,1984.0253164556962,1984.7215189873418,1985.4177215189873,1986.113924050633,1986.8101265822784,1987.506329113924,1988.2025316455697,1988.8987341772151,1989.5949367088608,1990.2911392405063,1990.987341772152,1991.6835443037974,1992.379746835443,1993.0759493670887,1993.7721518987341,1994.4683544303798,1995.1645569620252,1995.860759493671,1996.5569620253164,1997.253164556962,1997.9493670886077,1998.6455696202531,1999.3417721518988,2000.0379746835442,2000.73417721519,2001.4303797468353,2002.126582278481,2002.8227848101267,2003.5189873417721,2004.2151898734178,2004.9113924050632,2005.607594936709,2006.3037974683543,2007.0],\n",
       "\"resid\":[-1.5330517510657273,-1.37237363582271,-1.2146148391878027,-1.06269467976896,-0.9195324761743381,-0.7880475470119016,-0.6711592108897935,-0.5717867864159951,-0.49220754246961257,-0.4302211336331495,-0.38172044128840554,-0.34259130100404145,-0.308719548348659,-0.27599101889090966,-0.24029154819939924,-0.19772268234916773,-0.14719083289210483,-0.0895639305330252,-0.025750155167512667,0.04334231330892782,0.11680529500070488,0.19373061001231992,0.2731811684698161,0.3533881982410123,0.4316464751739119,0.5052008186737643,0.5712960481459172,0.6271769829956275,0.6700884426282313,0.6973035113395095,0.7088547642165308,0.7098111610947754,0.7057776478814612,0.702359170483807,0.7051606748090335,0.7197871067643637,0.7518421427848002,0.8047408891967485,0.8752197589732997,0.9587456928667161,1.050785631629358,1.1468065160134737,1.242275286771432,1.3326588846555065,1.41355404429425,1.4812403458993602,1.5322211343251315,1.5629998842198112,1.5700800702315945,1.5499651670086998,1.4991586491993556,1.4149176754196127,1.3015813839133499,1.1673692077278162,1.0205403249631169,0.8693539137195383,0.7220691520971748,0.5869452181963127,0.47181972560631746,0.37662790502787125,0.29428671873283674,0.21746916804928407,0.13884825430539027,0.05109697882922787,-0.053111657051018946,-0.18097576565300633,-0.33341226337203034,-0.5023562987889025,-0.6790522701795907,-0.8547445758198404,-1.020677613985624,-1.168095782952694,-1.2882570549809935,-1.3760928617474453,-1.4351609017542697,-1.4702558027947739,-1.4861721926622005,-1.4877046991498282,-1.4796479500509223,-1.4667965731587458]\n",
       "}\n",
       "}],\n",
       "\"computation_messages\":[\"LOESS drew a random sample with max_n=1000, seed=37 in [smooth/smooth stat] layer\"]\n",
       "};\n",
       "           var plotContainer = document.getElementById(\"RLJTH1\");\n",
       "           window.letsPlotCall(function() {{\n",
       "               LetsPlot.buildPlotFromProcessedSpecs(plotSpec, -1, -1, plotContainer);\n",
       "           }});\n",
       "       })();    \n",
       "   </script>"
      ],
      "text/plain": [
       "<lets_plot.plot.core.PlotSpec at 0x250b351b888>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ggplot(resids_df, aes(x='year', y='resid')) \\\n",
    "+ geom_line(aes(group='country'), alpha=1/3) \\\n",
    "+ geom_smooth(method='loess', span=0.3) \\\n",
    "+ ggsize(800, 400)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "按大洲分面"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "   <div id=\"4KDqUa\"></div>\n",
       "   <script type=\"text/javascript\" data-lets-plot-script=\"plot\">\n",
       "       (function() {\n",
       "           var plotSpec={\n",
       "\"data\":{\n",
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       "},\n",
       "\"mapping\":{\n",
       "\"x\":\"year\",\n",
       "\"y\":\"resid\",\n",
       "\"group\":\"country\"\n",
       "},\n",
       "\"data_meta\":{\n",
       "},\n",
       "\"facet\":{\n",
       "\"name\":\"wrap\",\n",
       "\"facets\":\"continent\",\n",
       "\"ncol\":3,\n",
       "\"order\":1,\n",
       "\"dir\":\"h\"\n",
       "},\n",
       "\"ggsize\":{\n",
       "\"width\":900,\n",
       "\"height\":500\n",
       "},\n",
       "\"kind\":\"plot\",\n",
       "\"scales\":[],\n",
       "\"layers\":[{\n",
       "\"geom\":\"line\",\n",
       "\"mapping\":{\n",
       "},\n",
       "\"data_meta\":{\n",
       "},\n",
       "\"color\":\"#4169E1\",\n",
       "\"alpha\":0.3333333333333333,\n",
       "\"data\":{\n",
       "}\n",
       "}]\n",
       "};\n",
       "           var plotContainer = document.getElementById(\"4KDqUa\");\n",
       "           window.letsPlotCall(function() {{\n",
       "               LetsPlot.buildPlotFromProcessedSpecs(plotSpec, -1, -1, plotContainer);\n",
       "           }});\n",
       "       })();    \n",
       "   </script>"
      ],
      "text/plain": [
       "<lets_plot.plot.core.PlotSpec at 0x250b36fc088>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ggplot(resids_df, aes(x='year', y='resid', group='country')) \\\n",
    "+ geom_line(color='#4169E1', alpha=1/3) \\\n",
    "+ facet_wrap('continent', ncol=3) \\\n",
    "+ ggsize(900, 500)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "从上图可以看出，波动剧烈的曲线几乎都发生在非洲和亚洲"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>continent</th>\n",
       "      <th>country</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Africa</td>\n",
       "      <td>Botswana</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Africa</td>\n",
       "      <td>Central African Republic</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Africa</td>\n",
       "      <td>Congo, Rep.</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Africa</td>\n",
       "      <td>Cote d'Ivoire</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Africa</td>\n",
       "      <td>Gabon</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Africa</td>\n",
       "      <td>Kenya</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>Africa</td>\n",
       "      <td>Lesotho</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>Africa</td>\n",
       "      <td>Namibia</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>Africa</td>\n",
       "      <td>Rwanda</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>Africa</td>\n",
       "      <td>South Africa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>Africa</td>\n",
       "      <td>Swaziland</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>Africa</td>\n",
       "      <td>Uganda</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>Africa</td>\n",
       "      <td>Zambia</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>Africa</td>\n",
       "      <td>Zimbabwe</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>Asia</td>\n",
       "      <td>Cambodia</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>Asia</td>\n",
       "      <td>China</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>Asia</td>\n",
       "      <td>Iraq</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>Asia</td>\n",
       "      <td>Korea, Dem. Rep.</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>Asia</td>\n",
       "      <td>Myanmar</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>Europe</td>\n",
       "      <td>Bulgaria</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   continent                   country\n",
       "0     Africa                  Botswana\n",
       "1     Africa  Central African Republic\n",
       "2     Africa               Congo, Rep.\n",
       "3     Africa             Cote d'Ivoire\n",
       "4     Africa                     Gabon\n",
       "5     Africa                     Kenya\n",
       "6     Africa                   Lesotho\n",
       "7     Africa                   Namibia\n",
       "8     Africa                    Rwanda\n",
       "9     Africa              South Africa\n",
       "10    Africa                 Swaziland\n",
       "11    Africa                    Uganda\n",
       "12    Africa                    Zambia\n",
       "13    Africa                  Zimbabwe\n",
       "14      Asia                  Cambodia\n",
       "15      Asia                     China\n",
       "16      Asia                      Iraq\n",
       "17      Asia          Korea, Dem. Rep.\n",
       "18      Asia                   Myanmar\n",
       "19    Europe                  Bulgaria"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 筛选残差绝对值大于等于5的所有国家\n",
    "(resids_df.query(\"resid >= 5 or resid <= -5\")\n",
    " .reindex(['continent', 'country'], axis=1)\n",
    " .drop_duplicates(subset=['continent', 'country'])\n",
    " .reset_index(drop=True)\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## $R^2$分析"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>country</th>\n",
       "      <th>continent</th>\n",
       "      <th>rsquared</th>\n",
       "      <th>rsquared_adj</th>\n",
       "      <th>f_pvalue</th>\n",
       "      <th>RMSE</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>Rwanda</td>\n",
       "      <td>Africa</td>\n",
       "      <td>0.017160</td>\n",
       "      <td>-0.081124</td>\n",
       "      <td>6.848927e-01</td>\n",
       "      <td>43.010899</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Botswana</td>\n",
       "      <td>Africa</td>\n",
       "      <td>0.034023</td>\n",
       "      <td>-0.062574</td>\n",
       "      <td>5.660414e-01</td>\n",
       "      <td>37.358712</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>51</th>\n",
       "      <td>Zimbabwe</td>\n",
       "      <td>Africa</td>\n",
       "      <td>0.056232</td>\n",
       "      <td>-0.038145</td>\n",
       "      <td>4.580290e-01</td>\n",
       "      <td>51.918232</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50</th>\n",
       "      <td>Zambia</td>\n",
       "      <td>Africa</td>\n",
       "      <td>0.059836</td>\n",
       "      <td>-0.034180</td>\n",
       "      <td>4.435318e-01</td>\n",
       "      <td>20.509239</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45</th>\n",
       "      <td>Swaziland</td>\n",
       "      <td>Africa</td>\n",
       "      <td>0.068211</td>\n",
       "      <td>-0.024968</td>\n",
       "      <td>4.122530e-01</td>\n",
       "      <td>44.143949</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99</th>\n",
       "      <td>Pakistan</td>\n",
       "      <td>Asia</td>\n",
       "      <td>0.997250</td>\n",
       "      <td>0.996975</td>\n",
       "      <td>3.877363e-14</td>\n",
       "      <td>0.162356</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>137</th>\n",
       "      <td>Switzerland</td>\n",
       "      <td>Europe</td>\n",
       "      <td>0.997391</td>\n",
       "      <td>0.997130</td>\n",
       "      <td>2.978930e-14</td>\n",
       "      <td>0.046187</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>119</th>\n",
       "      <td>France</td>\n",
       "      <td>Europe</td>\n",
       "      <td>0.997625</td>\n",
       "      <td>0.997387</td>\n",
       "      <td>1.863068e-14</td>\n",
       "      <td>0.048421</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>Mauritania</td>\n",
       "      <td>Africa</td>\n",
       "      <td>0.997674</td>\n",
       "      <td>0.997442</td>\n",
       "      <td>1.676077e-14</td>\n",
       "      <td>0.166083</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>54</th>\n",
       "      <td>Brazil</td>\n",
       "      <td>Americas</td>\n",
       "      <td>0.998047</td>\n",
       "      <td>0.997852</td>\n",
       "      <td>6.990433e-15</td>\n",
       "      <td>0.106430</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>142 rows × 6 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "         country continent  rsquared  rsquared_adj      f_pvalue       RMSE\n",
       "38        Rwanda    Africa  0.017160     -0.081124  6.848927e-01  43.010899\n",
       "3       Botswana    Africa  0.034023     -0.062574  5.660414e-01  37.358712\n",
       "51      Zimbabwe    Africa  0.056232     -0.038145  4.580290e-01  51.918232\n",
       "50        Zambia    Africa  0.059836     -0.034180  4.435318e-01  20.509239\n",
       "45     Swaziland    Africa  0.068211     -0.024968  4.122530e-01  44.143949\n",
       "..           ...       ...       ...           ...           ...        ...\n",
       "99      Pakistan      Asia  0.997250      0.996975  3.877363e-14   0.162356\n",
       "137  Switzerland    Europe  0.997391      0.997130  2.978930e-14   0.046187\n",
       "119       France    Europe  0.997625      0.997387  1.863068e-14   0.048421\n",
       "30    Mauritania    Africa  0.997674      0.997442  1.676077e-14   0.166083\n",
       "54        Brazil  Americas  0.998047      0.997852  6.990433e-15   0.106430\n",
       "\n",
       "[142 rows x 6 columns]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rsquared_df = (nest1.reindex(['country', 'continent', 'rsquared', 'rsquared_adj', 'f_pvalue', 'RMSE'], axis=1)\n",
    "               .sort_values(by='rsquared')\n",
    "              )\n",
    "rsquared_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "   <div id=\"j4k2LC\"></div>\n",
       "   <script type=\"text/javascript\" data-lets-plot-script=\"plot\">\n",
       "       (function() {\n",
       "           var plotSpec={\n",
       "\"data\":{\n",
       "\"continent\":[\"Africa\",\"Africa\",\"Africa\",\"Africa\",\"Africa\",\"Africa\",\"Africa\",\"Africa\",\"Africa\",\"Africa\",\"Africa\",\"Africa\",\"Africa\",\"Africa\",\"Africa\",\"Asia\",\"Europe\",\"Asia\",\"Africa\",\"Asia\",\"Africa\",\"Africa\",\"Africa\",\"Europe\",\"Europe\",\"Americas\",\"Europe\",\"Europe\",\"Americas\",\"Africa\",\"Europe\",\"Africa\",\"Africa\",\"Africa\",\"Asia\",\"Africa\",\"Europe\",\"Asia\",\"Africa\",\"Europe\",\"Africa\",\"Africa\",\"Americas\",\"Europe\",\"Europe\",\"Africa\",\"Americas\",\"Europe\",\"Africa\",\"Asia\",\"Asia\",\"Americas\",\"Asia\",\"Asia\",\"Americas\",\"Asia\",\"Oceania\",\"Africa\",\"Americas\",\"Asia\",\"Africa\",\"Asia\",\"Africa\",\"Americas\",\"Europe\",\"Europe\",\"Europe\",\"Africa\",\"Africa\",\"Asia\",\"Asia\",\"Americas\",\"Asia\",\"Africa\",\"Europe\",\"Asia\",\"Europe\",\"Asia\",\"Americas\",\"Europe\",\"Europe\",\"Asia\",\"Asia\",\"Africa\",\"Asia\",\"Americas\",\"Americas\",\"Africa\",\"Oceania\",\"Africa\",\"Asia\",\"Europe\",\"Americas\",\"Americas\",\"Africa\",\"Africa\",\"Europe\",\"Asia\",\"Europe\",\"Americas\",\"Africa\",\"Africa\",\"Americas\",\"Europe\",\"Americas\",\"Asia\",\"Americas\",\"Asia\",\"Asia\",\"Americas\",\"Africa\",\"Asia\",\"Asia\",\"Europe\",\"Africa\",\"Africa\",\"Asia\",\"Asia\",\"Europe\",\"Africa\",\"Europe\",\"Europe\",\"Europe\",\"Americas\",\"Africa\",\"Africa\",\"Asia\",\"Asia\",\"Africa\",\"Europe\",\"Americas\",\"Americas\",\"Americas\",\"Americas\",\"Africa\",\"Africa\",\"Asia\",\"Asia\",\"Europe\",\"Europe\",\"Africa\",\"Americas\"],\n",
       "\"rsquared\":[0.01715963560833922,0.03402340112518121,0.056231961509286776,0.059836438597311026,0.06821086763820328,0.08485635366036925,0.2833724037499007,0.31246865254407774,0.34215382028022223,0.34820277656107024,0.4370216332637139,0.4425572867647214,0.493244478326913,0.5117563968799164,0.5196607855249761,0.5457842029238305,0.5465421664469035,0.6386922171050902,0.6801783934238155,0.7030630615828831,0.7642187635690065,0.7659959725421682,0.7742793155601732,0.7917482189930263,0.7950187495434942,0.798007444720418,0.8018652089960057,0.8055666594089028,0.805659036392992,0.8127662072203283,0.8396631464341391,0.8399544627864233,0.8444286333995076,0.8701050762272227,0.8712773396596069,0.8723755033239857,0.878805378277254,0.879377501867625,0.8878146296254137,0.8956982852817478,0.897686643734803,0.9058037268640873,0.9078191203235408,0.9105777681472832,0.9166819085626203,0.9187105007510866,0.9240671647350875,0.9324304706813977,0.9347845689455307,0.9417258169766828,0.9465063908167282,0.9465260723838484,0.9477122569401565,0.947714694741227,0.9511951603442287,0.9523542300405091,0.9535846432154778,0.9552593591228846,0.9556720054977396,0.9570711340804461,0.9572733404412311,0.9595956322018508,0.9601505409077332,0.9617476717852144,0.9629005739225094,0.9648945567306179,0.9660432721684256,0.9660718040414731,0.966601989284388,0.9667398101928707,0.9673843985942533,0.967873444605905,0.9684365151459601,0.9685026330404538,0.9690350829544742,0.9697500776479548,0.9703265663986191,0.9704808657769356,0.9706078148365741,0.9706679742940993,0.9719608467220282,0.9720843890213072,0.972301827346736,0.9743713440094597,0.9747946053763191,0.9768307174756108,0.9773002554046568,0.9783151771806223,0.9796477374521627,0.9807042181841996,0.9811724017931691,0.9822156581196534,0.9827971010228941,0.9829865000187529,0.983331491384015,0.9840987340936552,0.9841457386400696,0.9841651232903605,0.9844359619595342,0.9845415641995103,0.9845582940547233,0.9851172113303249,0.9852044388728111,0.9853326449013836,0.9859201560454929,0.9873130908312411,0.9876133766521656,0.9876510097651163,0.987947511279093,0.988474008847212,0.9892356155990335,0.989360868753721,0.989411887050692,0.9895056819346137,0.9903042423122255,0.9905441705636979,0.9914225975448617,0.991541708050435,0.9921340130723291,0.9921424277083563,0.9933661226818029,0.9938383497403838,0.9945405561203661,0.9945662580930408,0.9945831202415243,0.9946536426779389,0.99478289949836,0.9950153543231571,0.9954514045786077,0.9954821628544864,0.9955680955772934,0.9963855158748879,0.9966637684953865,0.9967761492002805,0.9968507636452284,0.9968686397986546,0.9971141808647497,0.9972496528723085,0.9973908599357847,0.9976245847160378,0.9976742960093304,0.9980474148819337]\n",
       "},\n",
       "\"mapping\":{\n",
       "},\n",
       "\"data_meta\":{\n",
       "},\n",
       "\"ggsize\":{\n",
       "\"width\":700,\n",
       "\"height\":400\n",
       "},\n",
       "\"kind\":\"plot\",\n",
       "\"scales\":[],\n",
       "\"layers\":[{\n",
       "\"geom\":\"boxplot\",\n",
       "\"mapping\":{\n",
       "\"x\":\"continent\",\n",
       "\"y\":\"rsquared\"\n",
       "},\n",
       "\"show_legend\":false,\n",
       "\"data_meta\":{\n",
       "},\n",
       "\"outlier_shape\":21,\n",
       "\"outlier_size\":4,\n",
       "\"size\":1,\n",
       "\"color\":\"#4169E1\",\n",
       "\"width\":0.5,\n",
       "\"data\":{\n",
       "\"..middle..\":[0.9017451852994451,NaN,NaN,NaN,NaN,NaN,0.9704808657769356,NaN,0.9696808246765467,NaN,NaN,0.9827971010228941,NaN,NaN,0.9666161903338202],\n",
       "\"..lower..\":[0.5025004376034147,NaN,NaN,NaN,NaN,NaN,0.947714694741227,NaN,0.9031380267145155,NaN,NaN,0.9556720054977396,NaN,NaN,0.9666161903338202],\n",
       "\"..upper..\":[0.983715112738835,NaN,NaN,NaN,NaN,NaN,0.987947511279093,NaN,0.9874191634179987,NaN,NaN,0.988474008847212,NaN,NaN,0.9666161903338202],\n",
       "\"..ymin..\":[0.01715963560833922,NaN,NaN,NaN,NaN,NaN,0.9417258169766828,NaN,0.7917482189930263,NaN,NaN,0.9078191203235408,NaN,NaN,0.9666161903338202],\n",
       "\"..ymax..\":[0.9976742960093304,NaN,NaN,NaN,NaN,NaN,0.9972496528723085,NaN,0.9976245847160378,NaN,NaN,0.9980474148819337,NaN,NaN,0.9666161903338202],\n",
       "\"continent\":[\"Africa\",\"Asia\",\"Asia\",\"Asia\",\"Asia\",\"Asia\",\"Asia\",\"Europe\",\"Europe\",\"Americas\",\"Americas\",\"Americas\",\"Oceania\",\"Oceania\",\"Oceania\"],\n",
       "\"rsquared\":[NaN,0.5457842029238305,0.6386922171050902,0.7030630615828831,0.8712773396596069,0.879377501867625,NaN,0.5465421664469035,NaN,0.798007444720418,0.805659036392992,NaN,0.9535846432154778,0.9796477374521627,NaN]\n",
       "}\n",
       "},{\n",
       "\"geom\":\"jitter\",\n",
       "\"mapping\":{\n",
       "\"x\":\"continent\",\n",
       "\"y\":\"rsquared\"\n",
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       "\"show_legend\":false,\n",
       "\"data_meta\":{\n",
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       "\"width\":0.25,\n",
       "\"color\":\"#FF00FF\",\n",
       "\"data\":{\n",
       "}\n",
       "}]\n",
       "};\n",
       "           var plotContainer = document.getElementById(\"j4k2LC\");\n",
       "           window.letsPlotCall(function() {{\n",
       "               LetsPlot.buildPlotFromProcessedSpecs(plotSpec, -1, -1, plotContainer);\n",
       "           }});\n",
       "       })();    \n",
       "   </script>"
      ],
      "text/plain": [
       "<lets_plot.plot.core.PlotSpec at 0x250b0c543c8>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# R方分布\n",
    "ggplot(rsquared_df) \\\n",
    "+ geom_boxplot(aes(x='continent', y='rsquared'),\n",
    "               outlier_shape=21, outlier_size=4, size=1, color='#4169E1', width=0.5, show_legend=False) \\\n",
    "+ geom_jitter(aes(x='continent', y='rsquared'), \n",
    "              sampling=None, color='#FF00FF', show_legend=False, width=0.25) \\\n",
    "+ ggsize(700, 400)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "   <div id=\"l0DrMM\"></div>\n",
       "   <script type=\"text/javascript\" data-lets-plot-script=\"plot\">\n",
       "       (function() {\n",
       "           var plotSpec={\n",
       "\"data\":{\n",
       "\"continent\":[\"Africa\",\"Africa\",\"Africa\",\"Africa\",\"Africa\",\"Africa\",\"Africa\",\"Africa\",\"Africa\",\"Africa\",\"Africa\",\"Africa\",\"Africa\",\"Africa\",\"Africa\",\"Asia\",\"Europe\",\"Asia\",\"Africa\",\"Asia\",\"Africa\",\"Africa\",\"Africa\",\"Europe\",\"Europe\",\"Americas\",\"Europe\",\"Europe\",\"Americas\",\"Africa\",\"Europe\",\"Africa\",\"Africa\",\"Africa\",\"Asia\",\"Africa\",\"Europe\",\"Asia\",\"Africa\",\"Europe\",\"Africa\",\"Africa\",\"Americas\",\"Europe\",\"Europe\",\"Africa\",\"Americas\",\"Europe\",\"Africa\",\"Asia\",\"Asia\",\"Americas\",\"Asia\",\"Asia\",\"Americas\",\"Asia\",\"Oceania\",\"Africa\",\"Americas\",\"Asia\",\"Africa\",\"Asia\",\"Africa\",\"Americas\",\"Europe\",\"Europe\",\"Europe\",\"Africa\",\"Africa\",\"Asia\",\"Asia\",\"Americas\",\"Asia\",\"Africa\",\"Europe\",\"Asia\",\"Europe\",\"Asia\",\"Americas\",\"Europe\",\"Europe\",\"Asia\",\"Asia\",\"Africa\",\"Asia\",\"Americas\",\"Americas\",\"Africa\",\"Oceania\",\"Africa\",\"Asia\",\"Europe\",\"Americas\",\"Americas\",\"Africa\",\"Africa\",\"Europe\",\"Asia\",\"Europe\",\"Americas\",\"Africa\",\"Africa\",\"Americas\",\"Europe\",\"Americas\",\"Asia\",\"Americas\",\"Asia\",\"Asia\",\"Americas\",\"Africa\",\"Asia\",\"Asia\",\"Europe\",\"Africa\",\"Africa\",\"Asia\",\"Asia\",\"Europe\",\"Africa\",\"Europe\",\"Europe\",\"Europe\",\"Americas\",\"Africa\",\"Africa\",\"Asia\",\"Asia\",\"Africa\",\"Europe\",\"Americas\",\"Americas\",\"Americas\",\"Americas\",\"Africa\",\"Africa\",\"Asia\",\"Asia\",\"Europe\",\"Europe\",\"Africa\",\"Americas\"],\n",
       "\"RMSE\":[43.01089853764566,37.358711720979024,51.91823150932409,20.509239440093236,44.14394929009329,35.211566871911444,15.41026019463867,22.508915778554705,10.161229296736568,5.902415865384615,24.60956019393932,19.20345005384616,12.422304905477814,3.1429310108391526,12.577664410372977,16.460032585664308,6.295666005244766,31.698512247202803,10.518434390209817,15.117914614219083,3.3658463911421954,2.594605221911416,5.252010897902057,1.689556797785523,1.409268310023319,2.729051646153837,7.583589265967329,2.137777365967362,4.226904155477898,16.43578508881123,2.628366364219099,3.7370904523309703,3.4712508142191445,2.310455721911425,14.876375049569805,3.354170597785491,3.2096775433566065,9.198045733100113,1.9796747069930078,5.0925373505827665,4.76884101212119,5.441869603846154,1.6096463400932497,3.9325330159674285,0.681437615384623,4.19058357342657,3.0298346103729616,1.3168834285547673,3.0283453884614966,1.50732365827509,4.359811137645671,2.1957381736597044,1.4952104477855674,1.182866705477854,2.301381995454594,3.107656993939362,0.6469743426573479,1.9433751324009205,3.7751934331002333,1.717222750582751,2.240184115734203,1.874691210372968,0.6797177296037255,2.3069016523310015,0.23978556643355947,1.0265243782051303,0.5052857479021053,2.655322312937089,1.3798989054778734,2.688244020512806,1.451717392657365,1.7202923437063091,2.9752570593241083,1.0971105479020866,1.2989283659673354,3.645201108274975,0.29899807750582885,3.929046341491825,2.40318409160839,0.15903191841491707,0.6059717659673614,4.332535234615362,1.3640130582750545,1.269299020629364,5.511787009324112,0.2848142369463891,2.4469860093240543,1.4301614282051323,0.38515501456877044,2.430656627971996,2.5147554285548113,0.12093711188811436,1.4228743977855136,0.15320775303029985,2.3712480869463968,0.597979591142168,0.2283445129370712,1.7676881785548417,0.19546847191142125,1.4029096467366151,0.4140750402097894,1.7503458946386838,1.0921984296037295,1.3157605236596333,0.17316746153845985,0.8840741911421672,0.7068870206293656,1.3788458999999995,0.5068007800699137,1.1608064400933498,1.316896252331041,0.9539249782051533,1.7256740153846775,0.17312221596736604,1.0799066363636403,0.8692975166666695,0.5468163115384737,0.8542567128205223,0.16598240384615542,0.4148366734266107,0.17367200233100535,0.12546949009323516,0.08579186538460726,0.4883977568764516,0.5729806757575631,0.3132130369463933,0.13376582750582738,0.44173692365968026,0.231941065734256,0.04484563636363828,0.08544349149184163,0.06212471153846394,0.3377689642191249,0.35810817960367586,0.2291027954545414,0.10803699160840481,0.41673201643354113,0.16235560384616093,0.04618693764568935,0.048420615967362704,0.16608258240092993,0.10642983566433684]\n",
       "},\n",
       "\"mapping\":{\n",
       "},\n",
       "\"data_meta\":{\n",
       "},\n",
       "\"ggsize\":{\n",
       "\"width\":700,\n",
       "\"height\":400\n",
       "},\n",
       "\"kind\":\"plot\",\n",
       "\"scales\":[],\n",
       "\"layers\":[{\n",
       "\"geom\":\"boxplot\",\n",
       "\"mapping\":{\n",
       "\"x\":\"continent\",\n",
       "\"y\":\"RMSE\"\n",
       "},\n",
       "\"show_legend\":false,\n",
       "\"data_meta\":{\n",
       "},\n",
       "\"outlier_shape\":21,\n",
       "\"outlier_size\":4,\n",
       "\"size\":1,\n",
       "\"color\":\"#4169E1\",\n",
       "\"width\":0.5,\n",
       "\"data\":{\n",
       "\"..middle..\":[NaN,NaN,NaN,NaN,NaN,2.8418338506992926,NaN,NaN,NaN,NaN,NaN,1.7256740153846775,NaN,NaN,NaN,NaN,0.5556287569347333,1.4029096467366151,NaN,NaN,0.5160646786130592],\n",
       "\"..lower..\":[NaN,NaN,NaN,NaN,NaN,1.1832047842657252,NaN,NaN,NaN,NaN,NaN,0.9539249782051533,NaN,NaN,NaN,NaN,0.16955230990676073,0.3377689642191249,NaN,NaN,0.5160646786130592],\n",
       "\"..upper..\":[NaN,NaN,NaN,NaN,NaN,11.470369647843816,NaN,NaN,NaN,NaN,NaN,3.929046341491825,NaN,NaN,NaN,NaN,1.549412553904421,2.3069016523310015,NaN,NaN,0.5160646786130592],\n",
       "\"..ymin..\":[NaN,NaN,NaN,NaN,NaN,0.10803699160840481,NaN,NaN,NaN,NaN,NaN,0.13376582750582738,NaN,NaN,NaN,NaN,0.04484563636363828,0.06212471153846394,NaN,NaN,0.5160646786130592],\n",
       "\"..ymax..\":[NaN,NaN,NaN,NaN,NaN,24.60956019393932,NaN,NaN,NaN,NaN,NaN,5.511787009324112,NaN,NaN,NaN,NaN,3.2096775433566065,4.226904155477898,NaN,NaN,0.5160646786130592],\n",
       "\"continent\":[\"Africa\",\"Africa\",\"Africa\",\"Africa\",\"Africa\",\"Africa\",\"Asia\",\"Asia\",\"Asia\",\"Asia\",\"Asia\",\"Asia\",\"Europe\",\"Europe\",\"Europe\",\"Europe\",\"Europe\",\"Americas\",\"Oceania\",\"Oceania\",\"Oceania\"],\n",
       "\"RMSE\":[43.01089853764566,37.358711720979024,51.91823150932409,44.14394929009329,35.211566871911444,NaN,16.460032585664308,31.698512247202803,15.117914614219083,14.876375049569805,9.198045733100113,NaN,6.295666005244766,7.583589265967329,5.0925373505827665,3.9325330159674285,NaN,NaN,0.6469743426573479,0.38515501456877044,NaN]\n",
       "}\n",
       "},{\n",
       "\"geom\":\"jitter\",\n",
       "\"mapping\":{\n",
       "\"x\":\"continent\",\n",
       "\"y\":\"RMSE\"\n",
       "},\n",
       "\"show_legend\":false,\n",
       "\"data_meta\":{\n",
       "},\n",
       "\"width\":0.25,\n",
       "\"color\":\"#FF00FF\",\n",
       "\"data\":{\n",
       "}\n",
       "}]\n",
       "};\n",
       "           var plotContainer = document.getElementById(\"l0DrMM\");\n",
       "           window.letsPlotCall(function() {{\n",
       "               LetsPlot.buildPlotFromProcessedSpecs(plotSpec, -1, -1, plotContainer);\n",
       "           }});\n",
       "       })();    \n",
       "   </script>"
      ],
      "text/plain": [
       "<lets_plot.plot.core.PlotSpec at 0x250b35cc2c8>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# RMSE分布\n",
    "ggplot(rsquared_df) \\\n",
    "+ geom_boxplot(aes(x='continent', y='RMSE'),\n",
    "               outlier_shape=21, outlier_size=4, size=1, color='#4169E1', width=0.5, show_legend=False) \\\n",
    "+ geom_jitter(aes(x='continent', y='RMSE'), \n",
    "              sampling=None, color='#FF00FF', show_legend=False, width=0.25) \\\n",
    "+ ggsize(700, 400)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "   <div id=\"9c1QUs\"></div>\n",
       "   <script type=\"text/javascript\" data-lets-plot-script=\"plot\">\n",
       "       (function() {\n",
       "           var plotSpec={\n",
       "\"data\":{\n",
       "\"continent\":[\"Africa\",\"Africa\",\"Africa\",\"Africa\",\"Africa\",\"Africa\",\"Africa\",\"Africa\",\"Africa\",\"Africa\",\"Africa\",\"Africa\",\"Africa\",\"Africa\",\"Africa\",\"Asia\",\"Europe\",\"Asia\",\"Africa\",\"Asia\",\"Africa\",\"Africa\",\"Africa\",\"Europe\",\"Europe\",\"Americas\",\"Europe\",\"Europe\",\"Americas\",\"Africa\",\"Europe\",\"Africa\",\"Africa\",\"Africa\",\"Asia\",\"Africa\",\"Europe\",\"Asia\",\"Africa\",\"Europe\",\"Africa\",\"Africa\",\"Americas\",\"Europe\",\"Europe\",\"Africa\",\"Americas\",\"Europe\",\"Africa\",\"Asia\",\"Asia\",\"Americas\",\"Asia\",\"Asia\",\"Americas\",\"Asia\",\"Oceania\",\"Africa\",\"Americas\",\"Asia\",\"Africa\",\"Asia\",\"Africa\",\"Americas\",\"Europe\",\"Europe\",\"Europe\",\"Africa\",\"Africa\",\"Asia\",\"Asia\",\"Americas\",\"Asia\",\"Africa\",\"Europe\",\"Asia\",\"Europe\",\"Asia\",\"Americas\",\"Europe\",\"Europe\",\"Asia\",\"Asia\",\"Africa\",\"Asia\",\"Americas\",\"Americas\",\"Africa\",\"Oceania\",\"Africa\",\"Asia\",\"Europe\",\"Americas\",\"Americas\",\"Africa\",\"Africa\",\"Europe\",\"Asia\",\"Europe\",\"Americas\",\"Africa\",\"Africa\",\"Americas\",\"Europe\",\"Americas\",\"Asia\",\"Americas\",\"Asia\",\"Asia\",\"Americas\",\"Africa\",\"Asia\",\"Asia\",\"Europe\",\"Africa\",\"Africa\",\"Asia\",\"Asia\",\"Europe\",\"Africa\",\"Europe\",\"Europe\",\"Europe\",\"Americas\",\"Africa\",\"Africa\",\"Asia\",\"Asia\",\"Africa\",\"Europe\",\"Americas\",\"Americas\",\"Americas\",\"Americas\",\"Africa\",\"Africa\",\"Asia\",\"Asia\",\"Europe\",\"Europe\",\"Africa\",\"Americas\"],\n",
       "\"f_pvalue\":[0.6848926924849069,0.5660413525854955,0.4580289825059743,0.4435317816393349,0.41225300053605723,0.3582863706001765,0.07480350220441297,0.05883744026139141,0.04573927793620083,0.04340981415222651,0.019246250506021217,0.018234544017997796,0.010876998153314743,0.008906650888339933,0.008161502291865552,0.006057439728693828,0.0060039023165430585,0.0018158889847829393,9.62781708619356E-4,6.555906662018087E-4,2.001786533260392E-4,1.9256769671667544E-4,1.6012066370938935E-4,1.0607982440023545E-4,9.784476543558252E-5,9.077910734391508E-5,8.22747931405643E-5,7.473229515434177E-5,7.455147723915227E-5,6.166125111473322E-5,2.8023327028577696E-5,2.7765753887408808E-5,2.4043683958936745E-5,9.638426621120543E-6,9.206216731706712E-6,8.815615663929559E-6,6.787253614581796E-6,6.62678995109135E-6,4.593498406165025E-6,3.179394974686448E-6,2.885051031853801E-6,1.901315061860422E-6,1.7048760448696376E-6,1.4627631902609576E-6,1.0243505987638965E-6,9.047505850987075E-7,6.418952475255808E-7,3.568258497117111E-7,2.985393392872279E-7,1.6955214407481405E-7,1.1028654266403224E-7,1.1008285990970867E-7,9.835212903053314E-8,9.832909927045822E-8,6.957280066892741E-8,6.166345518185372E-8,5.40732438121314E-8,4.496446163993194E-8,4.2921128293210644E-8,3.6539670075681754E-8,3.568405816742984E-8,2.6957841639444125E-8,2.5150790895907665E-8,2.0484703707692503E-8,1.756954771417158E-8,1.3317552269491804E-8,1.1271117291356788E-8,1.1223706971388282E-8,1.0371382348889657E-8,1.0158546642322583E-8,9.209050088223826E-9,8.537242856596894E-9,7.812980863284901E-9,7.731272421790137E-9,7.09790675360309E-9,6.31348401760628E-9,5.7329699832242034E-9,5.585088689659312E-9,5.46572520875571E-9,5.409878758337778E-9,4.315804687695125E-9,4.221337571719763E-9,4.059099189187955E-9,2.750551943107731E-9,2.530345798420105E-9,1.6592007438797697E-9,1.4974563311574965E-9,1.19080714690684E-9,8.667221611502723E-10,6.636418846824698E-10,5.868273529567231E-10,4.410957735290886E-10,3.7346100217943653E-10,3.5332193299252164E-10,3.188765895179595E-10,2.5185848482858995E-10,2.4815299884015386E-10,2.4663762856756144E-10,2.2622866588646558E-10,2.1864753176079566E-10,2.1746539953115318E-10,1.8081433631938368E-10,1.755708853214637E-10,1.6808572344376105E-10,1.3697879597367004E-10,8.131829463584497E-11,7.213048146032566E-11,7.104025705211202E-11,6.29037777109991E-11,5.030234243002829E-11,3.572758205705437E-11,3.369500990892853E-11,3.2894119487932216E-11,3.146149982861325E-11,2.117245853718711E-11,1.8677420349624663E-11,1.1466674133551991E-11,1.0691783934038952E-11,7.43523965862061E-12,7.395529324318117E-12,3.170601619516082E-12,2.191309830375038E-12,1.1962801177534575E-12,1.1683721960592682E-12,1.150347605881403E-12,1.0773583973407836E-12,9.532192666394362E-13,7.58885071252822E-13,4.800780619020814E-13,4.640583403853617E-13,4.215567447141457E-13,1.5205030113984425E-13,1.0185587127952597E-13,8.58142576925445E-14,7.633039682984899E-14,7.418790936285897E-14,4.931385915890463E-14,3.8773626708199813E-14,2.9789295176702E-14,1.8630675717630555E-14,1.6760773245476584E-14,6.990433217178234E-15]\n",
       "},\n",
       "\"mapping\":{\n",
       "},\n",
       "\"data_meta\":{\n",
       "},\n",
       "\"ggsize\":{\n",
       "\"width\":700,\n",
       "\"height\":400\n",
       "},\n",
       "\"kind\":\"plot\",\n",
       "\"scales\":[],\n",
       "\"layers\":[{\n",
       "\"geom\":\"boxplot\",\n",
       "\"mapping\":{\n",
       "\"x\":\"continent\",\n",
       "\"y\":\"f_pvalue\"\n",
       "},\n",
       "\"show_legend\":false,\n",
       "\"data_meta\":{\n",
       "},\n",
       "\"outlier_shape\":21,\n",
       "\"outlier_size\":4,\n",
       "\"size\":1,\n",
       "\"color\":\"#4169E1\",\n",
       "\"width\":0.5,\n",
       "\"data\":{\n",
       "\"..middle..\":[NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN,2.3931830468571113E-6,NaN,NaN,NaN,NaN,NaN,5.585088689659312E-9,NaN,NaN,NaN,NaN,NaN,NaN,NaN,6.4154383684136466E-9,NaN,NaN,NaN,NaN,NaN,3.7346100217943653E-10,NaN,NaN,2.7469982986640836E-8],\n",
       "\"..lower..\":[NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN,2.8536753717327473E-10,NaN,NaN,NaN,NaN,NaN,6.29037777109991E-11,NaN,NaN,NaN,NaN,NaN,NaN,NaN,9.977361163618715E-11,NaN,NaN,NaN,NaN,NaN,5.030234243002829E-11,NaN,NaN,2.7469982986640836E-8],\n",
       "\"..upper..\":[NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN,0.009891824520827338,NaN,NaN,NaN,NaN,NaN,9.832909927045822E-8,NaN,NaN,NaN,NaN,NaN,NaN,NaN,2.321079082473703E-6,NaN,NaN,NaN,NaN,NaN,4.2921128293210644E-8,NaN,NaN,2.7469982986640836E-8],\n",
       "\"..ymin..\":[NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN,1.6760773245476584E-14,NaN,NaN,NaN,NaN,NaN,3.8773626708199813E-14,NaN,NaN,NaN,NaN,NaN,NaN,NaN,1.8630675717630555E-14,NaN,NaN,NaN,NaN,NaN,6.990433217178234E-15,NaN,NaN,2.7469982986640836E-8],\n",
       "\"..ymax..\":[NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN,0.019246250506021217,NaN,NaN,NaN,NaN,NaN,1.6955214407481405E-7,NaN,NaN,NaN,NaN,NaN,NaN,NaN,3.179394974686448E-6,NaN,NaN,NaN,NaN,NaN,6.957280066892741E-8,NaN,NaN,2.7469982986640836E-8],\n",
       "\"continent\":[\"Africa\",\"Africa\",\"Africa\",\"Africa\",\"Africa\",\"Africa\",\"Africa\",\"Africa\",\"Africa\",\"Africa\",\"Africa\",\"Asia\",\"Asia\",\"Asia\",\"Asia\",\"Asia\",\"Asia\",\"Europe\",\"Europe\",\"Europe\",\"Europe\",\"Europe\",\"Europe\",\"Europe\",\"Europe\",\"Americas\",\"Americas\",\"Americas\",\"Americas\",\"Americas\",\"Americas\",\"Oceania\",\"Oceania\",\"Oceania\"],\n",
       "\"f_pvalue\":[0.6848926924849069,0.5660413525854955,0.4580289825059743,0.4435317816393349,0.41225300053605723,0.3582863706001765,0.07480350220441297,0.05883744026139141,0.04573927793620083,0.04340981415222651,NaN,0.006057439728693828,0.0018158889847829393,6.555906662018087E-4,9.206216731706712E-6,6.62678995109135E-6,NaN,0.0060039023165430585,1.0607982440023545E-4,9.784476543558252E-5,8.22747931405643E-5,7.473229515434177E-5,2.8023327028577696E-5,6.787253614581796E-6,NaN,9.077910734391508E-5,7.455147723915227E-5,1.7048760448696376E-6,6.418952475255808E-7,1.1008285990970867E-7,NaN,5.40732438121314E-8,8.667221611502723E-10,NaN]\n",
       "}\n",
       "},{\n",
       "\"geom\":\"jitter\",\n",
       "\"mapping\":{\n",
       "\"x\":\"continent\",\n",
       "\"y\":\"f_pvalue\"\n",
       "},\n",
       "\"show_legend\":false,\n",
       "\"data_meta\":{\n",
       "},\n",
       "\"width\":0.25,\n",
       "\"color\":\"#FF00FF\",\n",
       "\"data\":{\n",
       "}\n",
       "}]\n",
       "};\n",
       "           var plotContainer = document.getElementById(\"9c1QUs\");\n",
       "           window.letsPlotCall(function() {{\n",
       "               LetsPlot.buildPlotFromProcessedSpecs(plotSpec, -1, -1, plotContainer);\n",
       "           }});\n",
       "       })();    \n",
       "   </script>"
      ],
      "text/plain": [
       "<lets_plot.plot.core.PlotSpec at 0x250b3752588>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# p值分布\n",
    "ggplot(rsquared_df) \\\n",
    "+ geom_boxplot(aes(x='continent', y='f_pvalue'),\n",
    "               outlier_shape=21, outlier_size=4, size=1, color='#4169E1', width=0.5, show_legend=False) \\\n",
    "+ geom_jitter(aes(x='continent', y='f_pvalue'), \n",
    "              sampling=None, color='#FF00FF', show_legend=False, width=0.25) \\\n",
    "+ ggsize(700, 400)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "        vertical-align: top;\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>continent</th>\n",
       "      <th>country</th>\n",
       "      <th>data</th>\n",
       "      <th>rsquared</th>\n",
       "      <th>resid</th>\n",
       "      <th>f_pvalue</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Africa</td>\n",
       "      <td>Rwanda</td>\n",
       "      <td>country continent  year  lifeExp      pop...</td>\n",
       "      <td>0.017160</td>\n",
       "      <td>1284    -2.741949\n",
       "1285    -1.012791\n",
       "1286     0...</td>\n",
       "      <td>0.684893</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Africa</td>\n",
       "      <td>Botswana</td>\n",
       "      <td>country continent  year  lifeExp      po...</td>\n",
       "      <td>0.034023</td>\n",
       "      <td>156   -5.307115\n",
       "157   -3.614458\n",
       "158   -2.01580...</td>\n",
       "      <td>0.566041</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Africa</td>\n",
       "      <td>Zimbabwe</td>\n",
       "      <td>country continent  year  lifeExp       ...</td>\n",
       "      <td>0.056232</td>\n",
       "      <td>1692    -6.770244\n",
       "1693    -4.287139\n",
       "1694    -1...</td>\n",
       "      <td>0.458029</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Africa</td>\n",
       "      <td>Zambia</td>\n",
       "      <td>country continent  year  lifeExp       po...</td>\n",
       "      <td>0.059836</td>\n",
       "      <td>1680   -5.620026\n",
       "1681   -3.278900\n",
       "1682   -1.03...</td>\n",
       "      <td>0.443532</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Africa</td>\n",
       "      <td>Swaziland</td>\n",
       "      <td>country continent  year  lifeExp      ...</td>\n",
       "      <td>0.068211</td>\n",
       "      <td>1452    -4.980859\n",
       "1453    -3.439233\n",
       "1454    -2...</td>\n",
       "      <td>0.412253</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Africa</td>\n",
       "      <td>Lesotho</td>\n",
       "      <td>country continent  year  lifeExp      pop...</td>\n",
       "      <td>0.084856</td>\n",
       "      <td>876    -5.241026\n",
       "877    -2.809854\n",
       "878    -0.58...</td>\n",
       "      <td>0.358286</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>Africa</td>\n",
       "      <td>Cote d'Ivoire</td>\n",
       "      <td>country continent  year  lifeExp   ...</td>\n",
       "      <td>0.283372</td>\n",
       "      <td>360   -4.368859\n",
       "361   -3.029642\n",
       "362   -1.22142...</td>\n",
       "      <td>0.074804</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>Africa</td>\n",
       "      <td>South Africa</td>\n",
       "      <td>country continent  year  lifeExp   ...</td>\n",
       "      <td>0.312469</td>\n",
       "      <td>1404   -4.332282\n",
       "1405   -2.202079\n",
       "1406   -1.08...</td>\n",
       "      <td>0.058837</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  continent        country                                               data  \\\n",
       "0    Africa         Rwanda       country continent  year  lifeExp      pop...   \n",
       "1    Africa       Botswana        country continent  year  lifeExp      po...   \n",
       "2    Africa       Zimbabwe         country continent  year  lifeExp       ...   \n",
       "3    Africa         Zambia       country continent  year  lifeExp       po...   \n",
       "4    Africa      Swaziland          country continent  year  lifeExp      ...   \n",
       "5    Africa        Lesotho       country continent  year  lifeExp      pop...   \n",
       "6    Africa  Cote d'Ivoire             country continent  year  lifeExp   ...   \n",
       "7    Africa   South Africa             country continent  year  lifeExp   ...   \n",
       "\n",
       "   rsquared                                              resid  f_pvalue  \n",
       "0  0.017160  1284    -2.741949\n",
       "1285    -1.012791\n",
       "1286     0...  0.684893  \n",
       "1  0.034023  156   -5.307115\n",
       "157   -3.614458\n",
       "158   -2.01580...  0.566041  \n",
       "2  0.056232  1692    -6.770244\n",
       "1693    -4.287139\n",
       "1694    -1...  0.458029  \n",
       "3  0.059836  1680   -5.620026\n",
       "1681   -3.278900\n",
       "1682   -1.03...  0.443532  \n",
       "4  0.068211  1452    -4.980859\n",
       "1453    -3.439233\n",
       "1454    -2...  0.412253  \n",
       "5  0.084856  876    -5.241026\n",
       "877    -2.809854\n",
       "878    -0.58...  0.358286  \n",
       "6  0.283372  360   -4.368859\n",
       "361   -3.029642\n",
       "362   -1.22142...  0.074804  \n",
       "7  0.312469  1404   -4.332282\n",
       "1405   -2.202079\n",
       "1406   -1.08...  0.058837  "
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 筛选p值大于等于0.05, 然后根据R方排序\n",
    "exception_df = (nest1.reindex(['continent', 'country', 'data', 'rsquared', 'resid', 'f_pvalue'], axis=1)\n",
    "                .query(\"f_pvalue >= 0.05\")\n",
    "                .sort_values(by='rsquared')\n",
    "                .reset_index(drop=True)\n",
    "               )\n",
    "exception_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>country</th>\n",
       "      <th>continent</th>\n",
       "      <th>year</th>\n",
       "      <th>lifeExp</th>\n",
       "      <th>pop</th>\n",
       "      <th>gdpPercap</th>\n",
       "      <th>resid</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Rwanda</td>\n",
       "      <td>Africa</td>\n",
       "      <td>1952</td>\n",
       "      <td>40.0</td>\n",
       "      <td>2534927</td>\n",
       "      <td>493.323875</td>\n",
       "      <td>-2.741949</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Rwanda</td>\n",
       "      <td>Africa</td>\n",
       "      <td>1957</td>\n",
       "      <td>41.5</td>\n",
       "      <td>2822082</td>\n",
       "      <td>540.289398</td>\n",
       "      <td>-1.012791</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Rwanda</td>\n",
       "      <td>Africa</td>\n",
       "      <td>1962</td>\n",
       "      <td>43.0</td>\n",
       "      <td>3051242</td>\n",
       "      <td>597.473073</td>\n",
       "      <td>0.716366</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Rwanda</td>\n",
       "      <td>Africa</td>\n",
       "      <td>1967</td>\n",
       "      <td>44.1</td>\n",
       "      <td>3451079</td>\n",
       "      <td>510.963714</td>\n",
       "      <td>2.045523</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Rwanda</td>\n",
       "      <td>Africa</td>\n",
       "      <td>1972</td>\n",
       "      <td>44.6</td>\n",
       "      <td>3992121</td>\n",
       "      <td>590.580664</td>\n",
       "      <td>2.774681</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  country continent  year  lifeExp      pop   gdpPercap     resid\n",
       "0  Rwanda    Africa  1952     40.0  2534927  493.323875 -2.741949\n",
       "1  Rwanda    Africa  1957     41.5  2822082  540.289398 -1.012791\n",
       "2  Rwanda    Africa  1962     43.0  3051242  597.473073  0.716366\n",
       "3  Rwanda    Africa  1967     44.1  3451079  510.963714  2.045523\n",
       "4  Rwanda    Africa  1972     44.6  3992121  590.580664  2.774681"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# unnest列表列\n",
    "exception_resids = (exception_df.reindex(['data', 'resid'], axis=1)\n",
    "                    .apply(lambda x: x['data'].assign(resid=x['resid']), axis=1)\n",
    "                    .to_list()\n",
    "                   )\n",
    "exception_resids = pd.concat(exception_resids, axis=0, ignore_index=True)\n",
    "exception_resids.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "   <div id=\"wElzfe\"></div>\n",
       "   <script type=\"text/javascript\" data-lets-plot-script=\"plot\">\n",
       "       (function() {\n",
       "           var plotSpec={\n",
       "\"data\":{\n",
       "\"country\":[\"Rwanda\",\"Rwanda\",\"Rwanda\",\"Rwanda\",\"Rwanda\",\"Rwanda\",\"Rwanda\",\"Rwanda\",\"Rwanda\",\"Rwanda\",\"Rwanda\",\"Rwanda\",\"Botswana\",\"Botswana\",\"Botswana\",\"Botswana\",\"Botswana\",\"Botswana\",\"Botswana\",\"Botswana\",\"Botswana\",\"Botswana\",\"Botswana\",\"Botswana\",\"Zimbabwe\",\"Zimbabwe\",\"Zimbabwe\",\"Zimbabwe\",\"Zimbabwe\",\"Zimbabwe\",\"Zimbabwe\",\"Zimbabwe\",\"Zimbabwe\",\"Zimbabwe\",\"Zimbabwe\",\"Zimbabwe\",\"Zambia\",\"Zambia\",\"Zambia\",\"Zambia\",\"Zambia\",\"Zambia\",\"Zambia\",\"Zambia\",\"Zambia\",\"Zambia\",\"Zambia\",\"Zambia\",\"Swaziland\",\"Swaziland\",\"Swaziland\",\"Swaziland\",\"Swaziland\",\"Swaziland\",\"Swaziland\",\"Swaziland\",\"Swaziland\",\"Swaziland\",\"Swaziland\",\"Swaziland\",\"Lesotho\",\"Lesotho\",\"Lesotho\",\"Lesotho\",\"Lesotho\",\"Lesotho\",\"Lesotho\",\"Lesotho\",\"Lesotho\",\"Lesotho\",\"Lesotho\",\"Lesotho\",\"Cote d'Ivoire\",\"Cote d'Ivoire\",\"Cote d'Ivoire\",\"Cote d'Ivoire\",\"Cote d'Ivoire\",\"Cote d'Ivoire\",\"Cote d'Ivoire\",\"Cote d'Ivoire\",\"Cote d'Ivoire\",\"Cote d'Ivoire\",\"Cote d'Ivoire\",\"Cote d'Ivoire\",\"South Africa\",\"South Africa\",\"South Africa\",\"South Africa\",\"South Africa\",\"South Africa\",\"South Africa\",\"South Africa\",\"South Africa\",\"South Africa\",\"South Africa\",\"South Africa\"],\n",
       "\"year\":[1952.0,1957.0,1962.0,1967.0,1972.0,1977.0,1982.0,1987.0,1992.0,1997.0,2002.0,2007.0,1952.0,1957.0,1962.0,1967.0,1972.0,1977.0,1982.0,1987.0,1992.0,1997.0,2002.0,2007.0,1952.0,1957.0,1962.0,1967.0,1972.0,1977.0,1982.0,1987.0,1992.0,1997.0,2002.0,2007.0,1952.0,1957.0,1962.0,1967.0,1972.0,1977.0,1982.0,1987.0,1992.0,1997.0,2002.0,2007.0,1952.0,1957.0,1962.0,1967.0,1972.0,1977.0,1982.0,1987.0,1992.0,1997.0,2002.0,2007.0,1952.0,1957.0,1962.0,1967.0,1972.0,1977.0,1982.0,1987.0,1992.0,1997.0,2002.0,2007.0,1952.0,1957.0,1962.0,1967.0,1972.0,1977.0,1982.0,1987.0,1992.0,1997.0,2002.0,2007.0,1952.0,1957.0,1962.0,1967.0,1972.0,1977.0,1982.0,1987.0,1992.0,1997.0,2002.0,2007.0],\n",
       "\"resid\":[-2.7419487179490716,-1.0127913752917266,0.7163659673656326,2.0455233100229933,2.7746806526803525,3.403837995337696,4.850995337995059,2.8821526806524176,-17.309689976690226,-4.592532634032864,2.9626247086244746,6.020782051281834,-5.307115384615315,-3.614458041957967,-2.0158006993006055,-0.5411433566432464,1.8815139860140988,4.873171328671461,6.73482867132882,8.569486013986165,7.3891433566435225,-3.103199300699117,-9.328541958041768,-5.537884615384407,-6.77024358974375,-4.28713869463882,-1.933033799533895,0.1690710955710344,2.274175990675964,4.7782808857808945,7.932385780885824,10.385490675990752,8.876595571095656,-4.22629953379942,-10.581194638694491,-6.618089743589557,-5.620025641025933,-3.2788997669000395,-1.0307738927741426,1.016351981351761,3.6574778554776515,5.238603729603561,5.975729603729448,5.27785547785534,0.8589813519812495,-4.7008927738928605,-5.443766899766956,-1.9506410256410618,-4.980858974359094,-3.439233100233203,-2.3466072261073165,-1.1809813519814227,1.2626445221444627,3.772270396270322,6.3208962703962115,7.962522144522097,8.283148018647985,3.6227738927738784,-7.272600233100263,-12.003974358974375,-5.241025641025637,-2.809854312354304,-0.5876829836829671,-0.3205116550116358,0.47665967365970374,2.439831002331033,4.832002331002371,6.4561736596737305,8.483344988345067,3.8785163170163983,-7.564312354312264,-10.043141025640935,-4.368858974359007,-3.0296421911422087,-1.2214254079254445,0.5457913752913797,2.344008158508146,4.264224941724912,5.220441724941729,5.239658508158499,1.9758752913752602,-2.7299079254079146,-4.541691142191148,-3.698474358974323,-4.33228205128178,-2.2020792540789813,-1.0818764568761807,0.04832634032661787,0.9715291375294157,1.9567319347321614,3.7449347319349613,5.572137529137763,5.780340326340557,3.2825431235433555,-4.43425407925384,-9.306051282051044]\n",
       "},\n",
       "\"mapping\":{\n",
       "\"x\":\"year\",\n",
       "\"y\":\"resid\",\n",
       "\"group\":\"country\",\n",
       "\"color\":\"country\"\n",
       "},\n",
       "\"data_meta\":{\n",
       "},\n",
       "\"ggsize\":{\n",
       "\"width\":800,\n",
       "\"height\":400\n",
       "},\n",
       "\"kind\":\"plot\",\n",
       "\"scales\":[{\n",
       "\"aesthetic\":\"color\",\n",
       "\"palette\":\"Set2\",\n",
       "\"scale_mapper_kind\":\"color_brewer\"\n",
       "}],\n",
       "\"layers\":[{\n",
       "\"geom\":\"line\",\n",
       "\"mapping\":{\n",
       "},\n",
       "\"data_meta\":{\n",
       "},\n",
       "\"alpha\":0.5,\n",
       "\"size\":2,\n",
       "\"data\":{\n",
       "}\n",
       "}]\n",
       "};\n",
       "           var plotContainer = document.getElementById(\"wElzfe\");\n",
       "           window.letsPlotCall(function() {{\n",
       "               LetsPlot.buildPlotFromProcessedSpecs(plotSpec, -1, -1, plotContainer);\n",
       "           }});\n",
       "       })();    \n",
       "   </script>"
      ],
      "text/plain": [
       "<lets_plot.plot.core.PlotSpec at 0x250b35cc3c8>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 残差绘图\n",
    "ggplot(exception_resids, aes(x='year', y='resid', group='country', color='country')) \\\n",
    "+ geom_line(alpha=0.5, size=2) \\\n",
    "+ scale_color_brewer(palette='Set2') \\\n",
    "+ ggsize(800, 400)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "   <div id=\"HRSNCJ\"></div>\n",
       "   <script type=\"text/javascript\" data-lets-plot-script=\"plot\">\n",
       "       (function() {\n",
       "           var plotSpec={\n",
       "\"data\":{\n",
       "\"country\":[\"Rwanda\",\"Rwanda\",\"Rwanda\",\"Rwanda\",\"Rwanda\",\"Rwanda\",\"Rwanda\",\"Rwanda\",\"Rwanda\",\"Rwanda\",\"Rwanda\",\"Rwanda\",\"Botswana\",\"Botswana\",\"Botswana\",\"Botswana\",\"Botswana\",\"Botswana\",\"Botswana\",\"Botswana\",\"Botswana\",\"Botswana\",\"Botswana\",\"Botswana\",\"Zimbabwe\",\"Zimbabwe\",\"Zimbabwe\",\"Zimbabwe\",\"Zimbabwe\",\"Zimbabwe\",\"Zimbabwe\",\"Zimbabwe\",\"Zimbabwe\",\"Zimbabwe\",\"Zimbabwe\",\"Zimbabwe\",\"Zambia\",\"Zambia\",\"Zambia\",\"Zambia\",\"Zambia\",\"Zambia\",\"Zambia\",\"Zambia\",\"Zambia\",\"Zambia\",\"Zambia\",\"Zambia\",\"Swaziland\",\"Swaziland\",\"Swaziland\",\"Swaziland\",\"Swaziland\",\"Swaziland\",\"Swaziland\",\"Swaziland\",\"Swaziland\",\"Swaziland\",\"Swaziland\",\"Swaziland\",\"Lesotho\",\"Lesotho\",\"Lesotho\",\"Lesotho\",\"Lesotho\",\"Lesotho\",\"Lesotho\",\"Lesotho\",\"Lesotho\",\"Lesotho\",\"Lesotho\",\"Lesotho\",\"Cote d'Ivoire\",\"Cote d'Ivoire\",\"Cote d'Ivoire\",\"Cote d'Ivoire\",\"Cote d'Ivoire\",\"Cote d'Ivoire\",\"Cote d'Ivoire\",\"Cote d'Ivoire\",\"Cote d'Ivoire\",\"Cote d'Ivoire\",\"Cote d'Ivoire\",\"Cote d'Ivoire\",\"South Africa\",\"South Africa\",\"South Africa\",\"South Africa\",\"South Africa\",\"South Africa\",\"South Africa\",\"South Africa\",\"South Africa\",\"South Africa\",\"South Africa\",\"South Africa\"],\n",
       "\"year\":[1952.0,1957.0,1962.0,1967.0,1972.0,1977.0,1982.0,1987.0,1992.0,1997.0,2002.0,2007.0,1952.0,1957.0,1962.0,1967.0,1972.0,1977.0,1982.0,1987.0,1992.0,1997.0,2002.0,2007.0,1952.0,1957.0,1962.0,1967.0,1972.0,1977.0,1982.0,1987.0,1992.0,1997.0,2002.0,2007.0,1952.0,1957.0,1962.0,1967.0,1972.0,1977.0,1982.0,1987.0,1992.0,1997.0,2002.0,2007.0,1952.0,1957.0,1962.0,1967.0,1972.0,1977.0,1982.0,1987.0,1992.0,1997.0,2002.0,2007.0,1952.0,1957.0,1962.0,1967.0,1972.0,1977.0,1982.0,1987.0,1992.0,1997.0,2002.0,2007.0,1952.0,1957.0,1962.0,1967.0,1972.0,1977.0,1982.0,1987.0,1992.0,1997.0,2002.0,2007.0,1952.0,1957.0,1962.0,1967.0,1972.0,1977.0,1982.0,1987.0,1992.0,1997.0,2002.0,2007.0],\n",
       "\"lifeExp\":[40.0,41.5,43.0,44.1,44.6,45.0,46.218,44.02,23.599,36.087,43.413,46.242,47.622,49.618,51.52,53.298,56.024,59.319,61.484,63.622,62.745,52.556,46.634,50.728,48.451,50.469,52.358,53.995,55.635,57.674,60.363,62.351,60.377,46.809,39.989,43.487,42.038,44.077,46.023,47.768,50.107,51.386,51.821,50.821,46.1,40.238,39.193,42.384,41.407,43.424,44.992,46.633,49.552,52.537,55.561,57.678,58.474,54.289,43.869,39.613,42.138,45.047,47.747,48.492,49.767,52.208,55.078,57.18,59.685,55.558,44.593,42.592,40.477,42.469,44.93,47.35,49.801,52.374,53.983,54.655,52.044,47.991,46.832,48.328,45.009,47.985,49.951,51.927,53.696,55.527,58.161,60.834,61.888,60.236,53.365,49.339]\n",
       "},\n",
       "\"mapping\":{\n",
       "\"x\":\"year\",\n",
       "\"y\":\"lifeExp\",\n",
       "\"group\":\"country\",\n",
       "\"color\":\"country\"\n",
       "},\n",
       "\"data_meta\":{\n",
       "},\n",
       "\"ggsize\":{\n",
       "\"width\":800,\n",
       "\"height\":400\n",
       "},\n",
       "\"kind\":\"plot\",\n",
       "\"scales\":[{\n",
       "\"aesthetic\":\"color\",\n",
       "\"palette\":\"Set2\",\n",
       "\"scale_mapper_kind\":\"color_brewer\"\n",
       "}],\n",
       "\"layers\":[{\n",
       "\"geom\":\"line\",\n",
       "\"mapping\":{\n",
       "},\n",
       "\"data_meta\":{\n",
       "},\n",
       "\"alpha\":0.5,\n",
       "\"size\":2,\n",
       "\"data\":{\n",
       "}\n",
       "}]\n",
       "};\n",
       "           var plotContainer = document.getElementById(\"HRSNCJ\");\n",
       "           window.letsPlotCall(function() {{\n",
       "               LetsPlot.buildPlotFromProcessedSpecs(plotSpec, -1, -1, plotContainer);\n",
       "           }});\n",
       "       })();    \n",
       "   </script>"
      ],
      "text/plain": [
       "<lets_plot.plot.core.PlotSpec at 0x250b35e2488>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 原数据绘图\n",
    "ggplot(exception_resids, aes(x='year', y='lifeExp', group='country', color='country')) \\\n",
    "+ geom_line(alpha=0.5, size=2) \\\n",
    "+ scale_color_brewer(palette='Set2') \\\n",
    "+ ggsize(800, 400)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "全是非洲国家，艾滋病流行或许是影响预期寿命的其中一个因素， 1994年卢旺达(Rwanda)大屠杀也对预期寿命有显著的影响。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## RMSE分析\n",
    "亚洲国家的$R^2$并不低，但是RMSE较大。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>continent</th>\n",
       "      <th>country</th>\n",
       "      <th>data</th>\n",
       "      <th>RMSE</th>\n",
       "      <th>rsquared</th>\n",
       "      <th>resid</th>\n",
       "      <th>f_pvalue</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>80</th>\n",
       "      <td>Asia</td>\n",
       "      <td>Cambodia</td>\n",
       "      <td>country continent  year  lifeExp       p...</td>\n",
       "      <td>31.698512</td>\n",
       "      <td>0.638692</td>\n",
       "      <td>216     2.401577\n",
       "217     2.371063\n",
       "218     2.44...</td>\n",
       "      <td>0.001816</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>86</th>\n",
       "      <td>Asia</td>\n",
       "      <td>Iraq</td>\n",
       "      <td>country continent  year  lifeExp       pop...</td>\n",
       "      <td>16.460033</td>\n",
       "      <td>0.545784</td>\n",
       "      <td>732   -4.793462\n",
       "733   -2.852514\n",
       "734   -1.00856...</td>\n",
       "      <td>0.006057</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>90</th>\n",
       "      <td>Asia</td>\n",
       "      <td>Korea, Dem. Rep.</td>\n",
       "      <td>country continent  year  lifeExp...</td>\n",
       "      <td>15.117915</td>\n",
       "      <td>0.703063</td>\n",
       "      <td>828   -4.849603\n",
       "829   -2.406735\n",
       "830   -1.41386...</td>\n",
       "      <td>0.000656</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>81</th>\n",
       "      <td>Asia</td>\n",
       "      <td>China</td>\n",
       "      <td>country continent  year   lifeExp         ...</td>\n",
       "      <td>14.876375</td>\n",
       "      <td>0.871277</td>\n",
       "      <td>288   -3.190482\n",
       "289    0.704904\n",
       "290   -7.99627...</td>\n",
       "      <td>0.000009</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>96</th>\n",
       "      <td>Asia</td>\n",
       "      <td>Myanmar</td>\n",
       "      <td>country continent  year  lifeExp       p...</td>\n",
       "      <td>9.198046</td>\n",
       "      <td>0.879378</td>\n",
       "      <td>1044   -5.092551\n",
       "1045   -1.672027\n",
       "1046   -0.63...</td>\n",
       "      <td>0.000007</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   continent           country  \\\n",
       "80      Asia          Cambodia   \n",
       "86      Asia              Iraq   \n",
       "90      Asia  Korea, Dem. Rep.   \n",
       "81      Asia             China   \n",
       "96      Asia           Myanmar   \n",
       "\n",
       "                                                 data       RMSE  rsquared  \\\n",
       "80        country continent  year  lifeExp       p...  31.698512  0.638692   \n",
       "86      country continent  year  lifeExp       pop...  16.460033  0.545784   \n",
       "90                country continent  year  lifeExp...  15.117915  0.703063   \n",
       "81      country continent  year   lifeExp         ...  14.876375  0.871277   \n",
       "96        country continent  year  lifeExp       p...   9.198046  0.879378   \n",
       "\n",
       "                                                resid  f_pvalue  \n",
       "80  216     2.401577\n",
       "217     2.371063\n",
       "218     2.44...  0.001816  \n",
       "86  732   -4.793462\n",
       "733   -2.852514\n",
       "734   -1.00856...  0.006057  \n",
       "90  828   -4.849603\n",
       "829   -2.406735\n",
       "830   -1.41386...  0.000656  \n",
       "81  288   -3.190482\n",
       "289    0.704904\n",
       "290   -7.99627...  0.000009  \n",
       "96  1044   -5.092551\n",
       "1045   -1.672027\n",
       "1046   -0.63...  0.000007  "
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "exception_df2 = (nest1.reindex(['continent', 'country', 'data', 'RMSE', 'rsquared', 'resid', 'f_pvalue'], axis=1)\n",
    "                 .query(\"continent=='Asia'\")\n",
    "                 .sort_values(by='RMSE', ascending=False)\n",
    "                 .head()\n",
    "                )\n",
    "exception_df2.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "# unnest列表列\n",
    "exception_df2=exception_df2.query(\"RMSE >= 10\")['data'].to_list()\n",
    "exception_df2=pd.concat(exception_df2, axis=0, ignore_index=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "   <div id=\"68S9wR\"></div>\n",
       "   <script type=\"text/javascript\" data-lets-plot-script=\"plot\">\n",
       "       (function() {\n",
       "           var plotSpec={\n",
       "\"data\":{\n",
       "\"country\":[\"Cambodia\",\"Cambodia\",\"Cambodia\",\"Cambodia\",\"Cambodia\",\"Cambodia\",\"Cambodia\",\"Cambodia\",\"Cambodia\",\"Cambodia\",\"Cambodia\",\"Cambodia\",\"Iraq\",\"Iraq\",\"Iraq\",\"Iraq\",\"Iraq\",\"Iraq\",\"Iraq\",\"Iraq\",\"Iraq\",\"Iraq\",\"Iraq\",\"Iraq\",\"Korea, Dem. Rep.\",\"Korea, Dem. Rep.\",\"Korea, Dem. Rep.\",\"Korea, Dem. Rep.\",\"Korea, Dem. Rep.\",\"Korea, Dem. Rep.\",\"Korea, Dem. Rep.\",\"Korea, Dem. Rep.\",\"Korea, Dem. Rep.\",\"Korea, Dem. Rep.\",\"Korea, Dem. Rep.\",\"Korea, Dem. Rep.\",\"China\",\"China\",\"China\",\"China\",\"China\",\"China\",\"China\",\"China\",\"China\",\"China\",\"China\",\"China\"],\n",
       "\"year\":[1952.0,1957.0,1962.0,1967.0,1972.0,1977.0,1982.0,1987.0,1992.0,1997.0,2002.0,2007.0,1952.0,1957.0,1962.0,1967.0,1972.0,1977.0,1982.0,1987.0,1992.0,1997.0,2002.0,2007.0,1952.0,1957.0,1962.0,1967.0,1972.0,1977.0,1982.0,1987.0,1992.0,1997.0,2002.0,2007.0,1952.0,1957.0,1962.0,1967.0,1972.0,1977.0,1982.0,1987.0,1992.0,1997.0,2002.0,2007.0],\n",
       "\"lifeExp\":[39.417,41.366,43.415,45.415,40.317,31.22,50.957,53.914,55.803,56.534,56.752,59.723,45.32,48.437,51.457,54.459,56.95,60.413,62.038,65.044,59.461,58.811,57.046,59.545,50.056,54.081,56.656,59.942,63.983,67.159,69.1,70.647,69.978,67.727,66.662,67.297,44.0,50.54896,44.50136,58.38112,63.11888,63.96736,65.525,67.274,68.69,70.426,72.028,72.961]\n",
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       "\"mapping\":{\n",
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       "\"palette\":\"Set2\",\n",
       "\"scale_mapper_kind\":\"color_brewer\"\n",
       "}],\n",
       "\"layers\":[{\n",
       "\"geom\":\"line\",\n",
       "\"mapping\":{\n",
       "},\n",
       "\"data_meta\":{\n",
       "},\n",
       "\"alpha\":0.5,\n",
       "\"size\":2,\n",
       "\"data\":{\n",
       "}\n",
       "}]\n",
       "};\n",
       "           var plotContainer = document.getElementById(\"68S9wR\");\n",
       "           window.letsPlotCall(function() {{\n",
       "               LetsPlot.buildPlotFromProcessedSpecs(plotSpec, -1, -1, plotContainer);\n",
       "           }});\n",
       "       })();    \n",
       "   </script>"
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       "<lets_plot.plot.core.PlotSpec at 0x250b379f248>"
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     "execution_count": 27,
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   ],
   "source": [
    "# 原数据绘图\n",
    "ggplot(exception_df2, aes(x='year', y='lifeExp', group='country', color='country')) \\\n",
    "+ geom_line(alpha=0.5, size=2) \\\n",
    "+ scale_color_brewer(palette='Set2') \\\n",
    "+ ggsize(800, 400)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "亚洲RMSE最大的国家是柬埔寨。亚洲波动剧烈是因为发展快，人均寿命提高快，而不是非洲那种跌宕起伏。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 斜率与趋势\n",
    "&emsp;&emsp;很多时候，我们需要将上升和下降的曲线给分开，比如从一大堆商品销售历史数据中找出销量下降的商品，这时候也需要建模，然后通过拟合曲线的斜率，将上升和下降商品给分离出来(`model.params['year']`, `year`为时间变量)。当然只能是一次回归。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p style=\"color:blue; font-size:200%; font-weight:bold\">参考来源:</p>\n",
    "\n",
    "* [lets-plot.org](https://lets-plot.org/pages/api.html)\n",
    "* [statsmodels.org](https://www.statsmodels.org/v0.10.1/regression.html)\n",
    "* [Model basics](https://bookdown.org/ccolonescu/RPoE4/simplelm.html)\n",
    "* [Chapter 2 The Simple Linear Regression Model](https://r4ds.had.co.nz/model-basics.html#visualising-models)\n",
    "* [joblib.docs](https://joblib.readthedocs.io/en/latest/parallel.html)\n",
    "* [GLM Residual in Python statsmodel](https://stackoverflow.com/questions/66493682/glm-residual-in-python-statsmodel)\n",
    "* [What are pseudo r-squareds?](https://stats.idre.ucla.edu/other/mult-pkg/faq/general/faq-what-are-pseudo-r-squareds/)\n",
    "* [statsmodels_doc](https://tedboy.github.io/statsmodels_doc/generated/generated/statsmodels.genmod.generalized_linear_model.GLMResults.html)\n",
    "* [statmodels.org](https://www.statsmodels.org/stable/endog_exog.html)"
   ]
  }
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